The velocity function is v(t)=t^2−5t+4 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,5]. So I found the antiderivative of the function, which gave me t^3/3-5^2/2+4x+c. Then

134,975 results
  1. 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.

  2. CALCULUS PLEASE HELP!!!

    SHOW WORK PLEASE!!! The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin πt + 3 cos πt, where t is measured in seconds. (Round your answers to two decimal places.) (a)

  3. Calculus

    The velocity function is v(t)=t^2−5t+4 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,5]. So I found the antiderivative of the function, which gave me t^3/3-5^2/2+4x+c.

  4. Calculus

    The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2, v(0) = −3, 0 ≤ t ≤ 5 (a) Find the velocity at time t. v(t) = ______ m/s (b) Find the distance traveled during the given

  5. calculus

    a particle moves along a straight line and has an acceleration given by a(t) = 6t+4 where a is measured in cm/sec^2. Its initial velocity is -6 cm/sec. Initially it sits 9 cm to the right of the origin. Find its displacement function? Can anyone show me

  6. 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.

  7. 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.

  8. Calculus

    Let f be the function given by f(t) = 2ðt + sin(2ðt) a) Find the value of t in the open interval (0,20 for which the line tangent at (t, f(t)) is parallel to the line through (0,0) and (2,4ð) b) Suppose the given function describes the position of a

  9. math

    The velocity function, in feet per second, is given for a particle moving along a straight line. v(t) = 3t − 2, 0 ≤ t ≤ 3 Find the displacement 15/2 Find the total distance that the particle travels over the given interval Im not sure how to do this

  10. math

    Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x' (t) is its velocity, and x'' (t) is its acceleration. x(t) = t3 − 12t2 + 21t − 9, 0 ≤ t ≤ 10 Find the open t-intervals on which the particle is

  11. 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

  12. 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

  13. physics

    Two forces, 1 = (3.85 − 2.85) N and 2 = (2.95 − 3.65) N, act on a particle of mass 2.10 kg that is initially at rest at coordinates (−2.30 m, −3.60 m). (a) What are the components of the particle's velocity at t = 11.8 s? = m/s (b) In what

  14. Calculus

    The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2, v(0) = −3, 0 ≤ t ≤ 5 (a) Find the velocity at time t. v(t) = t^2+2t-3 m/s (b) Find the distance traveled during the given

  15. 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

  16. 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

  17. calculus

    A particle moves on the x-axis so that its velocity at any time t is given by v(t) = sin 2t. At t = 0, the particle is at the origin. a)For 0 ≤ t ≤ π, find all values of t for which the particle is moving to the left. b)Write an expression for the

  18. 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].

  19. calculus

    The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin(πt) + 2 cos(πt), where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average

  20. 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]

  21. 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

  22. AP Calculus

    A particle is moving along a horizontal straight line. The graph of the position function (the distance to the right of a fixed point as a function of time) is shown below. Answer the following questions only on the interval (0,8). 1. When is the particle

  23. Calculus

    The velocity function is v(t)=t^2-4t+3 for a particle moving along a line. Find the displacement of the particle during the time interval [-1,6]

  24. Calc 1

    The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2, v(0) = −3, 0 ≤ t ≤ 4 (a) Find the velocity at time t. (b) Find the distance traveled during the given time interval.

  25. calculus

    The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin(πt) + 2 cos(πt), where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average

  26. 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

  27. univercity of baghdad

    A particle travels along a straight line with a velocity v=(12-3t^2)m/s.where t is in the seconds. When t=1s.the particle is located 10m to the left of the origin. Determine the acceleration when t=4s.the displacement from t=0s to t=10s.and the distance

  28. calc

    The velocity function, in feet per second, is given for a particle moving along a straight line. v(t) = t3 − 10t2 + 27t − 18, 1 ≤ t ≤ 7 Find the displacement Find the total distance that the particle travels over the given interval.

  29. 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

  30. 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

  31. Calculus (math)

    The velocity function (in meters per second) for a particle moving along a line is given by v(t)=t3−5t2. Find the displacement and the distance traveled by the particle during the time interval [-1,6]. Distance traveled = ?? I got 2089/12m as answer but

  32. 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

  33. 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]

  34. Physics

    a particle moving in the xy plane has velocity components dx/dt =2t and dy/dt = 4. If the particle starts from the origin at t = 0,magnitude of its displacement at t=2 is

  35. physics

    the velocity of a particle moving along the axis is given for t>0 by v=(32t -2t^3 ) m/s where t is in s what is the acceleration of a particle when (after t=0 ) it achieves its maximum displacement in the positive x direction

  36. physics

    A particle moving in simple harmonic motion passes through the equilibrium point (x=0) 9 times per second. At t=0t=0 its velocity at x=−0.01 m is negative. It travels 0.4 m in a complete cycle. The particle's position as a function of time is described

  37. Calculus..

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

  38. maths

    the displacement of a particle moving in straight line is given by x= 16t-2t^2 find out displacement travelled after 2 and 6 second

  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

  40. calculus

    let f(t) = 2*pi*t + sin(2*pi*t) a) find value of t in open interval (0,2) for which the tangent line at (t, f(t)) is parallel to the line through (0,0( and (2, 4pi) b) suppose the given funtion describes the position of a particle on the x-axis for 0

  41. DYNAMICS

    A particle travels along a straight line with a velocity v=(12-3t^2) m/s, when t is in seconds. When t=1s, the particle is located 10m to the left of the origin. Determine the accelaration when t=4s, the displacement from t=0 to t=10s, and the distance the

  42. physics

    The equation of motion of a particle in vertical SHM is given by y = (10 cm) sin 0.80t. (a) What is the particle's displacement at t = 1.1 s? (b) What is the particle's velocity at t = 1.1 s? (c) What is the particle's acceleration at t = 1.1 s?

  43. 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].

  44. 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

  45. 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

  46. trig

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

  47. 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

  48. PHYSICS

    The position of a particle moving on a smooth horizontal floor is given as a function of time according to the equation x=ut+1/2at^2. At time t=0, the particle has the velocity u. Obtain an expression for the velocity as the function of time. Hence, find

  49. Calculus Answer Check

    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

  50. calc 1

    The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2, v(0) = −3, 0 ≤ t ≤ 3 (a) Find the velocity at time t. (b) Find the distance traveled during the given time interval.

  51. Please help with Calculus problem??

    A particle moves with a fixed acceleration 3 m/s^2. If its initial velocity is s(0)=0: a) Find its velocity function. b) How long does it take for the particle to reach the velocity 14 m/s^2? c) Find the distance the particle traveled when its velocity

  52. College Physics

    A particle is moving in the xy plane with constant acceleration. At t=o, the particle is given by x=4m, y=3m, and has a velocity v=2m/s x-hat - 9m/s y-hat. The acceleration of the particle is given by a=4m/s^2 x-hat + 3m/s^2 y-hat. Find the velocity vector

  53. 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

  54. calculus homework help stuck

    Let s(t) denote the position of a particle at time t, and let v and a be the velocity and acceleration respectively. The particle is moving according to the data a(t)=10sin(t)+3cos(t) s(0)=-4 s(2pi)=1 find a function describing position of particle

  55. Math

    A particle moves in a straight line with velocity t^(-2)-(1/16) ft/s. Find the total displacement and total distance traveled over the time interval [2,5 ok i got the displacement is .1125 ft however i can not find the distance! help!

  56. Please help me with M1 kinematics!

    A particle is travelling with velocity (4i+5j)m/s. It undergoes an acceleration of magnitude 2.5m/s^2 in a direction given by the vector (3i-4j). Find the velocity and displacement of the particle from its initial position after 4s.

  57. 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

  58. math

    The velocity function (in meters per second) for a particle moving along a line is given by v(t)=t3–4t2. Find the displacement and the distance traveled by the particle during the time interval [-1,6]. (Hint: Draw a graph of the velocity function.) Your

  59. Math: Calculus

    The velocity function is v(t)= t^2-5t+ 4 for a particle moving along a line. The position function s(t) is an antiderivative of the velocity function. Find the displacement, s(6) - s(-3), by the particle during the time interval [-3,6].

  60. 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].

  61. 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.

  62. 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

  63. 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 =

  64. 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

  65. 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

  66. 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

  67. 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.

  68. 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.

  69. math

    The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 6/t2, where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3.

  70. 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]

  71. 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

  72. 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

  73. CALCULUS

    The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 3sin(ðt) + 5cos(ðt), where t is measured in seconds. (Round all answers to the nearest hundredth.) (a) Find the average

  74. Physics

    1. A particle moving with simple harmonic motion has maximum displacement of 50 cm angular velocity of 1.02rad/s. Calculate the (a) the maximum velocity (b) maximum acceleration of the particle (c) the speed and acceleration of the particle when it is 30cm

  75. Dynamics

    The acceleration of a particle moving along a straight line is inversely proportional to its speed with the constant of porpotionality being k. The body starts from the position s = x0 ^i with initial speed v0. Determine the velocity of the particle as a

  76. Calculus

    A particle moves with a fixed acceleration of 3 m/s^2. If its initial velocity is v(0)= 2 m/s, and its initial displacement is s(0)= 0 A)Find its velocity function v(t) B)How long does it take for the particle to reach the velocity 14 m/s? C)Find the

  77. physics

    Particle moving under influence of a constant force is given by V =√|4-2X| where X is magnitude of displacement of the particle At t=0 initially the particle is noticed to be moving towards east.The distance travelled by the particle in first 5seconds

  78. calculus

    the function s(t)=(t^2+t)^2/3, t>0, represents the displacement s, in metres, of a particle moving along a straight line after t seconds

  79. 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.

  80. Maths (Calculus)

    The motion of a particle performing damped oscillations is given by the formula y = e-t sin2t Where y - displacement from its mean position and t - time in seconds (a)determine the time at which the velocity of the particle is 0 (b)Determine if the

  81. maths

    A particle with a velocity of 2m / s at t = 0 moves along a straight line with a constant acceleration of 0.2m / s s.find the displacement of the particle in10 second

  82. 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

  83. Calculus 1

    The acceleration function (in m/s^2) and the initial velocity are given for a particle moving along a line. a(t)=t+4, v(0)=4, 0 ≤ t ≤ 11 (a) Find the velocity at time t. (b) Find the distance traveled during the give time interval.

  84. Calc 1

    The acceleration function (in m/s^2) and the initial velocity are given for a particle moving along a line. a(t) = t + 6, v(0) = 4, 0 ≤ t ≤ 11 (a) Find the velocity at time t. (b) Find the distance traveled during the given time interval

  85. Calculus

    A particle moves in a straight line under a force such that its displacement s(t), in metres, at time t seconds, is given by s(t) = t3 − 5t2 + 3t +15 (i) Find the expression for the velocity of the particle. (ii) Find the time at which the particle is at

  86. Calculus and vectors

    Velocity represents the slope of a displacement function. Suppose an object was moving to the right, then stopped, then continued moving to the right. What would the displacement function look like?

  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

  88. Calculus

    A particle moves at varying velocity along a line and s=f(t) represents the particle's distance from a point as a function of time, t. Sketch a possible graph for f if the average velocity of the particle between t=2 and t=6 is the same as the

  89. 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(πt) + 2 cos(πt), where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average

  90. Science

    The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 3 sin(πt) + 5 cos(πt), where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average

  91. 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

  92. Calculus

    SHOW WORK PLEASE!!!!! The displacement (in centimetres) of a particle moving back and forth along a straight line is given by the equation of motion s = 4 sin(πt) + 2 cos(πt), where t is measured in seconds. (Round your answers to two decimal places.)

  93. Calc I

    A particle moves at varying velocity along a line and s= f(t) represents the particle's distance from a point as a function of time, t. sketch a graph for f if the average velocity of the particle between t=2 and t=6 is the same as the instantaneous

  94. Calculus

    The position of a particle moving along the x-axis as a function of time,t, is given by x(t)=(1/6)t^3-t^2+3t-1 for t≥0. The particle's velocity becomes three times its initial velocity when t=? I know v(t)=x'(t)=(1/2)t^2-2t+3=9, but I do not understand

  95. physics

    The displacement of a particle in centimeters is given by y=8 sin (2πft). If f=20 Hz, find the displacement and the velocity of the particle at a time t=0.01 s and 0.07 s. (ans: y=7.61 cm, v=3.11 m/s, y=4.70 cm, v= -8.13 m/s) After I plug in f to get w

  96. calculus

    A particle p moves in a straight line with a velocity v m/sec that is given by v=4t^2-1 where t is the time after passing through a fixed point O on the line .find the instant when p is instantaneously at rest .also find at that instant ,displacement of p

  97. Physics

    A particle moving along a straight line with a constant acceleration of -4m/s*2 passes through a point A with a velocity of +8m/s at some movement find the distance travelled by the particle in 5sec after that movement? Ans:26m

  98. 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

  99. physics

    If velocity v of particle moving in straight line is related with distance travelled S as v=2(1+S)^1/2. What will the acceleration of the particle?

  100. phsics

    A charged particle is moving in a uniform magnetic field. Which of the following statements concerning the magnetic force exerted on the particle is false? A) It does not change the kinetic energy of the particle. B) It can act only on a particle in

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