Solve: The posistion of a particle moving along a coordinate line is s=sqrt(5+4t), with s in meters and t in seconds. Find the particle's velocity at t=1 sec. A) 2/3 m/sec B) 4/3 m/sec C) -1/3 m/sec D) 1/6 m/sec

146,370 results

1. Calculus

Solve: The posistion of a particle moving along a coordinate line is s=sqrt(5+4t), with s in meters and t in seconds. Find the particle's velocity at t=1 sec. A) 2/3 m/sec B) 4/3 m/sec C) -1/3 m/sec D) 1/6 m/sec Thank you!
2. calculus

Me again. One last question! Again, just needed my answer verified with any explanation or walk-through. The position of a particle moving along a coordinate line is s=√(3+6t) with s in meters and t in seconds. find the particle's acceleration at t=1 second. a. 1 m/sec^2...
3. calculus

the position of a particle moving along a coordinate line is s=√(1+4t) , with s in metres and t in seconds. Find the particle's velocity and acceleration at t=6 sec
4. calculus

a particle moves along a number line measured in cm so that its position at time t sec is given by s=72/(t+2) +k, k is a constant and t>=0 seconds. (a) Find the instantaneous velocity of the particle at t=4 seconds (b) Find the acceleration of the particle when t =4 seconds...

A particle moves along a line so that its position at any time t >= 0 is given by the function -t^3 + t^2 + 5t + 3, where p is measured in feet and t is measured in seconds. 1. Find the displacement during the first four seconds. My answer: 75 ft 2. Find the average ...
6. physics help

The magnitude of the velocity of a particle which starts from rest 2 ft below the origin when t = 0 and moves along a vertical axis is directly proportional to the time after starting. The displacement of the particle during the time interval from t = 1 sec to t = 2 sec is 3 ...
7. physics help

The magnitude of the velocity of a particle which starts from rest 2 ft below the origin when t = 0 and moves along a vertical axis is directly proportional to the time after starting. The displacement of the particle during the time interval from t = 1 sec to t = 2 sec is 3 ...
8. Calculus

The velocity of a particle moving along the x-axis is given by f(t)=6-2t cm/sec. Use a graph of f(t)to find the exact change in position of the particle from time t=0 to t=4 seconds.
9. physics

The position of a particle moving along an x axis is given by x = 15t2 - 2.0t3, where x is in meters and t is in seconds. (a) Determine the position, velocity, and acceleration of the particle at t = 3.0 s. x = m v = m/s a = m/s2 (b) What is the maximum positive coordinate ...
10. Calculus

The position of a particle moving on a horizontal line is given by s(t)=2t^3-15t^2+24t-5, where s is measured in feet and t in seconds. a: What is the initial position of the particle? b: What is the average velocity of the particle on the interval [0,2]?Indicate units of ...
11. physics

the motion of a particle along a straight line is described by the function x=(2t-3)^2 where x is in metres and t is in seconds. A)find the position ,veocity and acceleration at t=2 sec. B) find the velocity of the particle at origin.
12. math

A particle moves along straight line such that its displacement S meters from a given point is S = t^3 – 5t^2 + 4 whee t is time in seconds. Find (a) The displacement of particle at t = 5 (b) The velocity of the particle when t = 5 (c) The values of t when the particle is ...
13. Calculus

Sorry this is really long. Just wondering how I would do each of these A particle is moving with velocity v(t) = t^2 – 9t + 18 with distance, s measured in meters, left or right of zero, and t measured in seconds, with t between 0 and 8 seconds inclusive. The position at ...
14. calculus

velocity of a particle- the displacement s (in meters) of a particle moving in a straight line is given by the equation of motion s=4t^3+6t+2, where t is measured in seconds. Find the velocity of the particle s at times t=a t=1 t=2 t=3
15. Calculus

A particle moves along a line so that its posistion at any t is greater than or equal to 0 is given by the function s(t)= t^3-8t+1, where s is measured in feet and t is measured in seconds. a) find the displacement during the first three seconds b) Find the average velocity ...
16. math

The displacement (in meters) of a particle moving in a straight line is given by s = 4 t^3 where t is measured in seconds. Find the average velocity of the particle over the time interval [ 7 , 9]. Find the (instantaneous) velocity of the particle when t = 7.
17. Calculus

1) A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t) = (t)In(2t). Find the acceleration of the particle when the velocity is first zero. 2) The driver of a car traveling at 50 ft/sec suddenly applies the brakes. The position of the car is s...
18. Calculus

The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 5/t2, where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3. (a) Find the average velocity during each time period. (...
19. Calculus

The displacement (in meters) of a particle moving in a straight line is given by s=2t^3 where is measured in seconds. Find the average velocity of the particle over the time interval [10,13]. the average velocity is 798 What is the instantaneous velocity of the particle when t...
20. Calculus

The position of a function of a moving particle is s(t)=5+4t-t^2 for 0<t<10 where s is in meters and t is measured in seconds. What is the maximum speed in m/sec of the particle on the interval [0,10]?
21. calculus

The velocity of a particle moving along the t-axis is given by f(t)=2+.05t cm/sec. Use a graph of y=f(t) to find the exact change in position (distance traveled) for the particle from t=2 to t=8.

The following table gives the velocity v(t) (in feet per sec) at different instances of time t (in sec) of a particle moving along a horizontal axis. t 0 4 8 12 16 20 v(t) 43 42 40 35 25 5 Estimate the distance traveled by the particle between t = 0 sec and t = 20 sec using 5 ...
23. AP Calculus

The position of a particle moving on the x-axis at time t>0 seconds is: x(t)= e^t - t^1/2. a) Find the average velocity of the particel over the interval [1,3]. b) In what direction and how fast is the particle moving at t= 1 seconds? c) For what values of t is the particle...
24. math

(a)find antiderivatives for the following functions : (i) e^5x sinh3x + 4x+6/x^2+3x+5 . (ii)root3x(x^2-2/x+1). (b)Evaluate the following integrals over the given intervals: (i)4/2x-1 - 3/x+4 over [1,3] (ii)cosh 3x-sinh4x over [0, ln2] (c)A particle is moving from rest with an ...
25. math

heeeeelp meeeee ... (a)find antiderivatives for the following functions : (i) e^5x sinh3x + 4x+6/x^2+3x+5 . (ii) ã3x(x^2-2/x+1). (b)Evaluate the following integrals over the given intervals: (i)4/2x-1 - 3/x+4 over [1,3] (ii)cosh 3x-sinh4x over [0, ln2] (c)A particle is ...
26. math

weloo (a)find antiderivatives for the following functions : (i) e^5x sinh3x + 4x+6/x^2+3x+5 . (ii)root3x(x^2-2/x+1). (b)Evaluate the following integrals over the given intervals: (i)4/2x-1 - 3/x+4 over [1,3] (ii)cosh 3x-sinh4x over [0, ln2] (c)A particle is moving from rest ...
27. math

For 4.95 seconds , a particle moves in a straight line according to the position function: s(t) = e^t(5-t)-5 . a. when id the particle at rest ? when is particle moving forward ? b. Find the total distance traveled by the particle in intervals [0,1] seconds and [1,2] seconds...
28. math

For 4.95 seconds , a particle moves in a straight line according to the position function: s(t) = e^t(5-t)-5 . a. when id the particle at rest ? when is particle moving forward ? b. Find the total distance traveled by the particle in intervals [0,1] seconds and [1,2] seconds...
29. calulus

a particle is moving along the cure y=sqrt x. as the particle passes through the point (4,2), its x-coordinate increase at a rate of 3 cm/s. how fast is the distancefrom the particle to the origin changing at this instant?
30. Calculus

I don't understand what the graph is suppose to show and what the integral equation is suppose to mean. How would I use the graph to answer the questions? f is the differentiable function whose graph is shown in the figure. The position at time t (sec) of a particle moving ...
31. calculus

A particle is moving along the curve below. y = sqrt(x) As the particle passes through the point (4,2), its x-coordinate increases at a rate of 4 cm/s. How fast is the distance from the particle to the origin changing at this instant?
32. Calc

A particle is moving along the curve y= 3 \sqrt{3 x + 4}. As the particle passes through the point (4, 12), its x-coordinate increases at a rate of 4 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
33. Calculus 1

A particle is moving along the curve y= 4 \sqrt{3 x + 1}. As the particle passes through the point (1, 8), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
34. Calculus HELP

A particle is moving along the curve y=5 sqrt (2x+6). As the particle passes through the point (5,20 , its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
35. Calc

A particle is moving along the curve y= 4 sqrt{2 x + 2}. As the particle passes through the point (1, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
36. Math

A particle is moving along the curve y= 2 \sqrt{4 x + 4}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
37. Math

A particle is moving along the x axis so that its distance x in meters,at time t seconds,is x(t)=3,2(sqrt of tan (5t)).Find its velocity at time t=1,5 seconds.
38. Math

The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 4/t^2, where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3.
39. physics

The position vector r of a particle moving in the xy plane is r=2ti+2sin[(pi/4)t]j , with is in meters and t in seconds. (a) Calculate the x and y components of the particle's position at , and 4.0 s and sketch the particle's path in the plane for the interval . (b) Calculate ...
40. Calculus

A particle travels along the x-axis so that its velocity is given by v(t)=cos3x for 0<(or equal to)t<(or equal to)5. When t=0, the particle is at x=5. a. What is the smallest x-coordinate of the particle? b. What is the total distance traveled? c. At what t is the ...
41. Integral calculus

A particle is put inside an accelerator at time t=0. After t sec, its velocity is 10^5t^2 m/s. How far does the particle move during the first 10**-2 sec? distance= int velocity dt = INT 1E5 t^2 dt limits 0 to 1E-2 sec
42. math

Posted by weloo_volley on Wednesday, April 25, 2012 at 12:16am.heeeeelp meeeee ... (a)find antiderivatives for the following functions : (i) e^5x sinh3x + 4x+6/x^2+3x+5 . (ii) �ã3x(x^2-2/x+1). (b)Evaluate the following integrals over the given intervals: (i)4/2x...
43. Math

Context: The function v(t) represents the velocity of a particle moving along a horizontal line at any time, t, greater than or equal to zero. If the velocity is positive, the particle moves to the right. If the velocity is negative, the particle is moving to the left. The ...
44. Calculus, Related Rates

A particle at point A is 50 mm away from a second particle at point B. The first particle is moving toward point B at a constant rate and the second particle is moving at a right angle to the line AB at a rate that is 1/3 of the rate of the first particle. The particles get ...
45. Calculus

A particle moves on a vertical line so that its coordinate at time t is 3 y = t − 12t+ 3, t≥ 0 . When is the particle moving upward and when is it moving downward? Find the distance that the particle travels in the first 3 seconds. I got that t=2 and t=-2 and its ...
46. Calculus(math)

A particle is moving on a straight line in such a way that its velocity v is given by v(t)=2t+1 for 0≤t≤5 where t is measured in seconds and v in meters per second. What is the total distance traveled (in meters) by the particle between times t=0 seconds and t=5 ...
47. Calculus

A particle moves along a horizontal line so that at any time t its position is given by x(t)=cost-t. Time is measured in seconds and x is measured in meters. a.) Find the velocity as a function t. Use your answer to determine the velocity of the particle when t=pi/6 seconds. ...
48. Physics

A particle starts from the origin at t = 0 and moves along the positive x axis. A graph of the velocity of the particle as a function of the time is shown in the figure; the v-axis scale is set by vs = 7.0 m/s. (a) What is the coordinate of the particle at t = 5.0 s? (b) What ...
49. calculus

1. A particle moves along the x-axis, it's position at timer given by x(t)=t/(1+t^2), t greater than or equal to 0,where t is measured in seconds and x in meters. a) find the velocity at time t. I am a little confused.. Do I find the derivative by using the quotient rule? What...
50. Physics

A particle is moving along a straight line and its position is given by the relation x=( t3-6t2-15t+40)mm. Find:- (a). The time at which velocity is zero. (b). Position & displacement of the particle at that point. (c). Acceleration for the particle at that line.
51. physics

A particle is moving along a straight line and its position is given by the relation x=( t3-6t2-15t+40)mm. Find:- (a). The time at which velocity is zero. (b). Position & displacement of the particle at that point. (c). Acceleration for the particle at that line.
52. physics

A particle is moving along a straight line and its position is given by the relation x=(t3- 6t2- 15t+40) m FIND a) The time at which velocity is Zero, b) Position and displacement of the particle at that point. c) Acceleration for the particle at that line.
53. calculus

5. A particle moves along the y – axis with velocity given by v(t)=tsine(t^2) for t>=0 . a. In which direction (up or down) is the particle moving at time t = 1.5? Why? b. Find the acceleration of the particle at time t= 1.5. Is the velocity of the particle increasing at ...
54. science

the velocity of a particle is given by v=[16t^2i+4t^3j +(5t+2)k]m/s, where t is in seconds. If the particle is at the origin when t=0, determine the magnitude of the particle's acceleration when t=2s. What is the x,y,z coordinate position of the particle at this instant.
55. math

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 4 sin ¦Ðt + 3 cos ¦Ðt, where t is measured in seconds. (a)Find the average velocity during each time period. (i) [1, 2] (ii) [1, 1.1] (iii) [1...
56. Calculus

The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 3t − 7, 0 ≤ t ≤ 3 (a) Find the displacement. -7.5 m (b) Find the distance traveled by the particle during the given time interval.
57. Calculus

A particle moves on a vertical line. Its position, s, in metres at t seconds is given by s(t) = t^3 - 9t^2 + 24t, t>0/ I found the velocity and acceleration functions. s'(t) = 3t^2 - 18t + 24 s''(t) = 6t-18 b) When is the particle moving up? down? c) Find the distance the ...
58. Calculus: need clarification to where the #'s go

A particle is moving along the curve y= 2 \sqrt{4 x + 4}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant. *I just need step by ...
59. physics

A 0.150 kg particle moves along an x axis according to x(t) = -13.00 + 2.00t + 3.50t2 - 2.50t3, with x in meters and t in seconds. In unit-vector notation, what is the net force acting on the particle at t = 3.45 s? I tried solving using s=Vit + (.5)at^2 but I can't find the ...
60. Physics

A 0.150 kg particle moves along an x axis according to x(t) = -13.00 + 2.00t + 3.50t2 - 2.50t3, with x in meters and t in seconds. In unit-vector notation, what is the net force acting on the particle at t = 3.45 s? I tried solving using s=Vit + (.5)at^2 but I can't find the ...
61. physics

A proton (mass=1.67*10^-27 kg) moves with a velocity of 6.00*10^6 m/sec. Upon colliding with a stationary particle of unknown mass, the proton rebounds upon its own path with a velocity of 4.00*10^6 m/sec. The collision sends the unknown particle forward with a velocety of 2....
62. physics

A proton (mass=1.67*10^-27 kg) moves with a velocity of 6.00*10^6 m/sec. Upon colliding with a stationary particle of unknown mass, the proton rebounds upon its own path with a velocity of 4.00*10^6 m/sec. The collision sends the unknown particle forward with a velocety of 2....
63. Physics

The velocity graph of a particle moving along the x-axis is shown. The particle has zero velocity at t=0.00s and reaches a maximum velocity, vmax, after a total elapsed time, t total. If the initial position of the particle is x0 =6.22m, the maximum velocity of the particle is...
64. math

A particle moves with constant speed of 3m/sec along path y=3x^2 What is the acceleration of the particle at x=1.5m? I know that Velocity is y'=6x Somebody please help!
65. Urgent algebra help!

Here's my question. Please walk me through it so I can fully understand it. Jon begins jogging at a steady 3 meters/sec down the middle of Lane #1 of a public track. Laaura starts even with him in the center of Lane #2 but moves at 4 meters/sec. At the instant they begin, ...
66. math

The acceleration of a particle at a time t moving along the x-axis is give by: a(t) = 4e^(2t). At the instant when t=0, the particle is at the point x=2, moving with velocity v(t)=-2. Find the position of the particle at t=1/2 if you could show me how to get that please
67. math

A particle is traveling along a one-dimensional path (such as a number line). The position of the particle is governed by the time function x(t) ƒ­ 3t 4 ƒ{16t3 ƒy18t 2 ƒy 2 , where t is in minutes and 0 „T t „T 5 . Answer the following questions. a) At what times is ...

Here's my question. Please walk me through it so I can fully understand it. Jon begins jogging at a steady 3 meters/sec down the middle of Lane #1 of a public track. Laaura starts even with him in the center of Lane #2 but moves at 4 meters/sec. At the instant they begin, ...
69. Calculus (Derivatives)

Two particles are moving in straight lines. The displacement (in meters) of particle 1 is given by the function e^(4cos(t)) , where t is in seconds. The displacement (in meters) of particle 2 is given by the function -(t^3)/(3) - (t^2)/(2) + 2 , where t is in seconds. Find the...
70. Calculus AB

A particle is moving along the x-axis so that at time t its acceleration is a(t)=ðcos(ðt) At time t=1/2, the velocity v of the particle is 1/2. Find the velocity of the particle at any time t. I think I got that right, as sinðt + C. Now it wants the minimum velocity of the ...
71. Calculus III

A particle is moving in R2 according to the law x=t^2, y=t^3 (time is measured in seconds, coordinates in meters). (a) What is the average velocity of the particle over the time interval [1,1.1]? (b) What is the instantaneous velocity of the particle at time t=1?
72. physics

a particle with velocity of 2m/s at t= 0 moves along a straight line with constant acceleration of 0.2m/s2. find the displacement of the particle in 10 seconds
73. Calculus

The velocity function is v(t)=t^2-5t+6 for a particle moving along a line. Find the displacement of the particle during the time interval [-3,6].
74. Calculus

How would I solve this: -A particle moves along a line so that, at time t, its position is s(t)=8 sin2t. a) For what values of t does the particle change direction? b) What is the particle's maximum velocity?
75. Calculus

a particle starts at time t = 0 and moves along the x axis so that its position at any time t>= 0 is given by x(t) = ((t-1)^3)(2t-3) a.find the velocity of the particle at any time t>= 0 b. for what values of t is the velocity of the particle negative? c. find the value ...
76. acceleration estimate

t(sec) 1 1.5 2 2.5 v(ft/sec) 12.2 1.3 13.4 13.7 velocity of an object moving along a line at various times. How do I estimate the object's acceleration(in ft/sec^2) at t=1 TIA t(sec) 1, 1.5, 2, 2.5 v(ft/sec) 12.2 ,1.3 ,13.4 ,13.7 The second velocity of 1.3ft/sec is an error, ...
77. physic

The position function x(t) of a particle moving along an x axis is x = 6.00 - 8.00t2, with x in meters and t in seconds. (a) At what time and (b) where does the particle (momentarily) stop? At what (c) negative time and (d) positive time does the particle pass through the origin?
78. calculus

the displacement (in meter) of a particle moving in a straight line is given by the equation of motion s=5t^3+4t+2, where t is measured in seconds. Find the velocity of the particle at t=3.
79. math

The velocity function is v(t) = t^2 - 6 t + 8 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,6].
80. calculus

The velocity function is v(t) = - t^2 + 4 t - 3 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-2,6].
81. physics

A particle with a charge 7C and a mass of 20kg is traveling in a circular path around a fixed particle of charde -5C. The velocity is observed to be 3000m/sec. A 9C particle with the same velocity is instead in the presence of a uniform electric field of 250N/C as shown. What ...
82. physics

A 4.0 kg particle is moving along the x axis to the left with a velocity of v= -12.0 m/s. Suddenly, between times t =0 and t = 4.0 x a net force = 3t^2 – 12t is applied to the particle, where F is in N and t is in s. Calculate the velocity of the particle at t=4.0 s. Can I ...
83. calculus

A particle is moving along the curve y=4((3x+1)^.5). As the particle passes through the point (5,16) its -coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
84. Calculus

A particle is moving along the curve . As the particle passes through the point , its -coordinate increases at a rate of units per second. Find the rate of change of the distance from the particle to the origin at this instant.
85. Calculus

A particle is moving along the curve . As the particle passes through the point , its -coordinate increases at a rate of units per second. Find the rate of change of the distance from the particle to the origin at this instant.
86. Calculus

A particle is moving along the curve . As the particle passes through the point , its -coordinate increases at a rate of units per second. Find the rate of change of the distance from the particle to the origin at this instant.
87. math

The acceleration am/s^2 of a particle moving in a straight line is given by a = 18t – 4, where t is time in seconds. The initial velocity of the particle is 2 m/s a) Find the expression for velocity in terms of t b) Determine the time when the velocity is again 2m/s
88. Physics

A particle moved along the x axis with a constant acceleration of -85.0 meters per second squared. The initial position of the particle was at the origin and its initial velocity was +325 meters per second. Find the position of the particle at T=4.0 seconds. Please walk ...
89. calculus

A particle is moving along the curve y= 3sqrt3x+1. As the particle passes through the point (5,12), its x-coordinate increases at a rate of 3 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
90. Calculus

A particle is moving along the curve y = 2 √{3 x + 7}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
91. Calculus

A particle is moving along the curve y = 2 √{3 x + 7}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
92. Calculus

A particle is moving along the curve y = 2 √{3 x + 7}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 4 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
93. calculus

A particle is moving along the curve y=5sqrt(3x+1). As the particle passes through the point (5,20) its x-coordinate increases at a rate of 3 units per second. Find the rate of change of the distance from the particle to the origin at this instant.
94. Maths

A particle is moving along the curve y=4sqrt(4x+1) . As the particle passes through the point (2,12), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant. Thanks !!!
95. math

the velocity in m/sec of a particle moving along the x-axis is given by the function v(t) = 7cos3t, 0 < t < pi/2 Find the particle's displacement for the given time interval Displacement is the ending point minus the starting point. Ending point is at t=PI/2
96. Maths mst

Question – 3: Consider a particle moving according to the velocity function, v(t) = 2a-3exp(-2t)+2/t+2,for t>0. (a) If the net distance,d,covered by the particle in the time interval,[0,3],is 20,find the value of a. What is the terminal velocity of the particle?. (b) Find...
97. Math, Related Rates

Consider the hyperbola y = 1/x and think of it as a slide. A particle slides along the hyperbola so that its x-coordinate is increasing at a rate of f(x) units/sec. If its y-coordinate is decreasing at a constant rate of 1 unit/sec, what is f(x)? -I arrived at the answer f(x...
98. calculus

A particle that moves along a straight line has velocity v(t)=(t^2)e^(-2t) meters per second after t seconds.? How many meters will it travel during the first "t" seconds?
99. Calc 1

The velocity function (in meters per second) is given for a particle moving along a line. v(t) = t^2 − 2t − 15, 1 ≤ t ≤ 7 (a) Find the displacement. (b) Find the distance traveled by the particle during the given time interval.
100. Physics

At the moment t=0 a particle starts moving along thr x-axis so that its velocity projection varies as vx= 35 cos pi t cm/s, where 't' is expressed in seconds. Find the distance that this particle covers during t = 2.80 s after the start.