# Suppose the position of an object is given by ->r(vector) = (3.0t^2*ihat - 6.0t^3*jhat)m. Where t in seconds. Determine its velocity ->v as a function of time t. Determine its acceleration ->a as a function of time t. Determine ->r

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1. ## Physics-calc

Suppose the position of an object is given by ->r(vector) = (3.0t^2*ihat - 6.0t^3*jhat)m. Where t in seconds. Determine its velocity ->v as a function of time t. Determine its acceleration ->a as a function of time t. Determine ->r at time t =
2. ## Physics urgent help needed!

Suppose the position of an object is given by ->r(vector) = (3.0t^2*ihat - 6.0t^3*jhat)m. Where t in seconds. Determine its velocity ->v as a function of time t. Determine its acceleration ->a as a function of time t. Determine ->r at time t =
3. ## Repost physics

Suppose the position of an object is given by ->r(vector) = (3.0t^2*ihat - 6.0t^3*jhat)m. Where t in seconds. Determine its velocity ->v as a function of time t. Determine its acceleration ->a as a function of time t. Determine ->r at time t =
4. ## physics

At t= 0, a particle starts from rest at x= 0, y= 0, and moves in the xy plane with an acceleration ->a (vector) = (4.0ihat+ 3.0jhat)m/s^2. Assume t is in seconds. Determine the x component of velocity as a function of time t. Determine the y component
5. ## phys

At t= 0, a particle starts from rest at x= 0, y= 0, and moves in the xy plane with an acceleration ->a = (4.0ihat+ 3.0jhat)m/s^2. Assume t is in seconds. Determine the position of the particle as a function of time t. Express your answer in terms of the
6. ## physics

The coordinates of an object moving in the xy plane vary with time according to the equations x = −6.85 sin ùt and y = 4.00 − 6.85 cos ùt, where ù is a constant, x and y are in meters, and t is in seconds. (a) Determine the components of
7. ## physics

At the instant the displacement of a 2.00 kg object relative to the origin is d = (2.00 m) ihat + (4.00 m) jhat - (3.00 m) khat, its velocity is v = - (6.20 m/s) ihat + (2.70 m/s) jhat + (2.60 m/s) khat, and it is subject to a force F = (6.00 N) ihat -
8. ## physics

A particle moves through an xyz coordinate system while a force acts on it. When the particle has the position vector vector r = (2.00 m)ihat - (3.00 m)jhat + (2.00 m)khat, the force is vector F = Fxihat + (7.00 N)jhat - (5.30 N)khat and the corresponding
9. ## physics

A particle moves through an xyz coordinate system while a force acts on it. When the particle has the position vector vector r = (2.00 m)ihat - (3.00 m)jhat + (2.00 m)khat, the force is vector F = Fxihat + (7.00 N)jhat - (5.30 N)khat and the corresponding
10. ## Physics

In the time interval from 0.0 s to 10.1 s, the acceleration of a particle traveling in a straight line is given by ax = (0.1 m/s3)t. Let to the right be the +x direction. The particle initially has a velocity to the right of 10.0 m/s and is located 5.4 m
11. ## Physics

A particle starts from the origin with velocity 2i m/s at t = 0 and moves in the xy plane with a varying acceleration given by 2 (sq root t) where is in meters per second squared and t is in seconds. (a) Determine the velocity of the particle as a function
12. ## Physics-can anyone check my work?

A particle starts from the origin with velocity 2i m/s at t = 0 and moves in the xy plane with a varying acceleration given by 2 (sq root t) where is in meters per second squared and t is in seconds. (a) Determine the velocity of the particle as a function
13. ## physics

In this problem you will determine the average velocity of a moving object from the graph of its position as a function of time . A traveling object might move at different speeds and in different directions during an interval of time, but if we ask at
14. ## physics

The acceleration of a particle moving only on a horizontal plane is given by a= 3ti +4tj, where a is in meters per second-squared and t is in seconds. At t = 0s, the position vector r= (20.0 m)i + (40.0 m)j locates the particle, which then has the velocity
15. ## physics

The acceleration of a particle moving only on a horizontal plane is given by a= 3ti +4tj, where a is in meters per second-squared and t is in seconds. At t = 0s, the position vector r= (20.0 m)i + (40.0 m)j locates the particle, which then has the velocity
16. ## physics

At a certain instant, a particle-like object is acted on by a force F = (4.0 N) ihat - (3.0 N) jhat + (9.0 N) khat while the object's velocity is v = - (2.0 m/s) ihat + (4.0 m/s) khat. What is the instantaneous rate at which the force does work on the
17. ## 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
18. ## physics

The vector position of a particle varies in time according to the expression r with arrow = 6.60 i − 9.00t2 j where r with arrow is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (Use any

An object on Earth falls with an acceleration of a=9.81 m/s^2. A function exists between the height from which the object falls, the initial velocity of the object and the time the object spends in the air. h(t)= Vt + at^2 V=initial velocity. T= time. A=
20. ## Physics

At t = 0, a 785 g mass at rest on the end of a horizontal spring (k = 125 N/m) is struck by a hammer, which gives the mass an initial speed of 2.70 m/s. (a) Determine the period of the motion. T= .4979201367s Determine the frequency of the motion. f=
21. ## Calculus

Suppose you throw an object from a great height, so that it reaches very nearly terminal velocity by time it hits the ground. By measuring the impact, you determine that this terminal velocity is -49 m/sec. A. Write the equation representing the velocity
22. ## 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
23. ## 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
24. ## physics

an object's acceleration is given by the function a= 2/v^2, determine an expression for the velocity of the object as a function of time. (at t= 0, v=0)
25. ## physics

an object's acceleration is given by the function a= 2/v^2, determine an expression for the velocity of the object as a function of time. (at t= 0, v=0)
26. ## PHysics

A 3.00 kg object has a velocity (5.20 ihat - 2.40 jhat) m/s. (Note: From the definition of the dot product, v2 = vvec·vvec.) (a) What is its kinetic energy at this time? Could some one just please show me how to convert the velocity vector into the
27. ## phyics

Consulting the graph shown in (Figure 1) , determine the object's average velocity over the time interval from 2 to 4 seconds. Express your answer in meters per second to the nearest integer. Position versus time graph for an object traveling with a
28. ## Calculus

Suppose a certain object moves in a straight line with velocity v(t)= -2+t+3sin(pi t) where v is in meters per second and t is in seconds. Determine the net change in distance of the object from time t=0 to time t=6 seconds and find the object's average
29. ## phyics

Consulting the graph shown in (Figure 1) , determine the object's average velocity over the time interval from 2 to 4 seconds. Express your answer in meters per second to the nearest integer. Position versus time graph for an object traveling with a
30. ## college Physics

The coordinates of an object moving in the xy plane vary with time according to the following equations x = −7.16 sin ùt and y = 4.00 − 7.16 cos ùt, where ù is a constant, x and y are in meters, and t is in seconds. Write expressions for the
31. ## Calculus (Motion with Vector functions)

For the position function r(t)= (2+t^2,3t), determine the approximate angle between the acceleration and velocity vectors at (3,3). a)45.7 b)56.3 c)71.7 d)44.9 e)58.2
32. ## Terminal Velocity

How can u determine that a falling object has reached terminal velocity from a velocity time graph of its motion? u can determine if a falling object has reached terminal velocity from a velocity-time graph of its motion by its stop of acceleration. The
33. ## Calculus

The position of a particle, s metres from the starting point, after t seconds, is defined by the function s(t) = 2t^3 - 7t^2 + 4 a) determine the velocity of the particle after t seconds b) determine the velocity after 5 seconds
34. ## Physics

You have a mass of 2 kg attached to a spring with a spring constant 18 N/m. The mass is at rest at the equilibrium position. At time t=0 you hit the object with a hammer. This blow instantaneously gives the object a velocity of 3 m/s. The motion (after the
35. ## math(mechanics)

the acceleration of a particle as it moves along a straight line is given by a=(2t-1)m/s^2, where t is in seconds.if s=1m and v= 2m/s when t=0,determine the particles velocity and position when t=6s. Also, determine the total distance the particle travels
36. ## Physics

The position of an object as a function of time is r⃗ =(3.2t+ 1.8 t2)i^+(1.7t− 2.4 t2)j^m, where t is the time in seconds. Find the object’s magnitude of the acceleration. What is the direction of the acceleration?
37. ## 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
38. ## Calc

1. Differentiae each function a) Y=-3x^2+5x-4 b) F(x) = 6/x-3/x^2 c) F(x)=(3x^2-4x)(x^3+1) 2. Determine the equation of the tangent line to the curve y=2x^2-1 at the point where x=-2 3. Evaluate, rounding to two decimal places, If necessary a) In 5 b) b)
39. ## physics

The speed of a bullet as it travels down the barrel of a rifle toward the opening is given by v = (-4.25 107) t 2 + (3.45 105) t, where v is in meters per second and t is in seconds. The acceleration of the bullet just as it leaves the barrel is zero. (a)
40. ## science

The speed of a bullet as it travels down the barrel of a rifle toward the opening is given by v = (-4.25 10^7) t^2 + (3.45 10^5) t, where v is in meters per second and t is in seconds. The acceleration of the bullet just as it leaves the barrel is zero.
41. ## 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
42. ## 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
43. ## physics

Let ->V1= -6.1 ihat + 8.0 jhat and ->V2 = -4.8 jhat + 4.2 ihat. Determine the direction of ->V1 counterclockwise from the +x direction Determine the direction of ->V2 counterclockwise from the +x direction
44. ## 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
45. ## Physics

A particle is in uniform circular motion about the origin of an xy coordinate system, moving clockwise with a period of 3.50 s. At one instant, its position vector (from the origin) is r = (8.00 m) ihat - (7.00 m) jhat. At that instant, what is its
46. ## mitx 8.01x Classical Mechanics

An object is moving along a straight line parallel to the x-axis. Its position as a function of time is given by: x(t)=30 m−21 (ms) t+3 (ms2) t2 where the position x is in (m) and the time t is in (s). (a) What is the object's velocity at t=0 s, 2 s,
47. ## Grade 12 Calculus

Determine the velocity and acceleration as functions of time, t, for s(t) = 45t − 5t^2, where s(t) represents the distance as a function of time. (Hint: velocity and acceleration correspond to the first and second derivatives of the distance)
48. ## physics

An object moves to the right according to the equation x = 4t2 + 3t + 16 where x is in meters and t is in seconds. Determine the object's average velocity between time t = 0 and time t = 4 seconds.
49. ## calculus (gr 12)

Determine the velocity and acceleration as functions of time, t, for s(t) = 45t − 5t^2, where s(t) represents the distance as a function of time. (Hint: velocity and acceleration correspond to the first and second derivatives of the distance)
50. ## calculus (gr 12)

Determine the velocity and acceleration as functions of time, t, for s(t) = 45t − 5t^2, where s(t) represents the distance as a function of time. (Hint: velocity and acceleration correspond to the first and second derivatives of the distance)
51. ## Physics

The velocity vefot of a ball is v(t)=-3x+4y at any time. Its initial position is r=12x-4y. The components of the velocity vector are in m/s and the components of the position vector are in meters. The symbols x and y are the unit vetors in x and y
52. ## Physics

Automotive engineers refer to the time rate of change of acceleration as the "jerk." Assume an object moves in one dimension such that its jerk J is constant. (a) Determine expressions for its acceleration ax(t), velocity vx(t), and position x(t), given
53. ## calculus

after t seconds the position of a particle which is moving along a straight line is x=2t^3-9t^2+12t+6, when is the acceleration zero? determine the velocity at that time.
54. ## calculus 3

A ball is thrown northward into the air from the origin in three dimensional space ( the xy plane is the ground, the positive y-axis points north, positive x-axis is east and the positive z – axis is height above the ground ). The initial velocity of the
55. ## Physics

The vector position of a 3.45 g particle moving in the xy plane varies in time according to 1 = 3 + 3t + 2t2 where t is in seconds and is in centimeters. At the same time, the vector position of a 5.00 g particle varies as 2 = 3 − 2t2 − 6t.
56. ## Physics

The vector position of a 3.45 g particle moving in the xy plane varies in time according to 1 = 3 + 3t + 2t2 where t is in seconds and is in centimeters. At the same time, the vector position of a 5.00 g particle varies as 2 = 3 − 2t2 − 6t.
57. ## Physics

The vector position of a 3.45 g particle moving in the xy plane varies in time according to 1 = 3 + 3t + 2t2 where t is in seconds and is in centimeters. At the same time, the vector position of a 5.00 g particle varies as 2 = 3 − 2t2 − 6t.
58. ## Physics

The vector position of a 3.45 g particle moving in the xy plane varies in time according to 1 = 3 + 3t + 2t2 where t is in seconds and is in centimeters. At the same time, the vector position of a 5.00 g particle varies as 2 = 3 − 2t2 − 6t.
59. ## Calculus

The position, p(t), of an object at time t is given. Find the instantaneous velocity at the indicated time c. Also determine whether it is moving forward, backward, or neither at time c. p(t)=2-1/t at c=3
60. ## physics

The position of an object as a function of time is given by x = At2 – Bt + C, where A = 7.3 m/s2, B = 5.8 m/s, and C = 4.5 m. Find the instantaneous velocity and acceleration as functions of time. (Use the following as necessary: t.) help!!!!!!!!! thank
61. ## Physics

At t=0 a particle starts from rest at x=0, y=0 and moves in the xy plane with an acceleration a=(4.0i+3.0j)m/s^2. Determine (a) the x and y components of velocity, (b) the speed of the particle, and (c) the position of the particle, all as a function of
62. ## physics

an object moving on the x axis with a constant acceleration increases its x coordinate by 108 m in a time of 9.5 s and has a velocity of 20 m/s at the end of this time. Determine the acceleration of the object during this motion?
63. ## physics

A student observes an airplane fly overhead with a constant velocity parallel to the x-axis at a height of 7.60 × 103 m. At time t = 0 the airplane is directly above the student, the vector P~ o = 7.60 × 103ˆj m describes the position on the airplane
64. ## Calculus

s(t) = t^2 - 6t + 5 models the motion of a person cycling along Rte 66 where s(t) is the number of miles north of Los Angeles the person is at time t hours. 1) Write functions for the cyclist's velocity and acceleration at any time t. 2) Find the position
65. ## Physics

Suppose the position of an object at time t is (6 + 5t, 2t2, 7t − 5t3). (a) What is the instantaneous velocity at time t? (b) What is the acceleration at time t? (c) What is the instantaneous velocity at time t = 0? (d) What is the acceleration at
66. ## physics

An object moving on the x axis with a constant acceleration increases its x coordinate by 161 m in a time of 12.5 s and has a velocity of 20 m/s at the end of this time. Determine the acceleration of the object during this motion. Answer in units of m/s2.
67. ## Physics

A car starts from rest and accelerates at a rate of 1 m/s^2 until it reaches a velocity of 7 m/s. It then travels at a constant velocity for the next 15 seconds. The driver then applies the brake, bringing the car to stop. The brakes provide an
68. ## physics

The acceleration of a certain particle is a function of time: a(t) = pt^2-qt^3, where p and q are constants. Initially, the velocity and position of the particle are zero. (a) What is the velocity as a function of time? (b) What is the position as a
69. ## physics

The position of an object as a function of time is given as x = At3 + Bt2 + Ct + D. The constants are A = 2.3m/s3, B = 1.8m/s2, C = −4.3m/s, and D = 2 m.(a) What is the velocity of the object at t = 12s? (b) What is the acceleration of the object at t =
70. ## Calculus-derivatives

Explain how to do these questions~ 1. An object moves in a straight line with its position at time t seconds given by s(t) = 3-2t+t^2, where s is the measured in metres. At what time is the object not moving? 2. Determine the coordinates of the point(s) on
71. ## Physics

A race car moves such that its position fits the relationship x=(5m/s) t + (.75m/s3 ) t3 where x is measured in meters and t in seconds. A)Plot a graph of position versus time. B)Determine the instantaneous velocity at t=4s using time intervals of .4s,
72. ## Math

The acceleration a(t) of a moving object is given by the derivative of the velocity function v(t). Find the acceleration of the object at time t=5 seconds if v(t)=12tsquared+8t meters per second. Thanks for any help.
73. ## Math

The acceleration of an object g = -9.8 m/s^2. From the top of a building of 245 m., an object is thrown upwards at an initial velocity of 12m/s (a) What is the function for the velocity of the object? I put vf^2 = Vi^2 + 2a(yf-yi) vf^2 = 216.09 + 19.6 (yf
74. ## Physics

Consider a 4.6 kilogram object moves from the origin always to the right (call that x-axis). Its speed increases uniformly (means constant acceleration) from zero to 0.667 metres/sec. 1.Describe how its velocity changes: initial, final and whether it
75. ## 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
76. ## Physics

A potential energy function for a two-dimensional force is of the form U = 3 x^(4)y - 8 x. Find the force that acts at the point (x, y). (Use x and y as appropriate.) I know its something about partial derivatives but I'm not sure how to go about it. And
77. ## math

The height h(in ft) above the ground of a submarine-launches missile is given by the function h=-16t+96t+80 where t represents the time in seconds. Scetch a graph of this function. Determine the time at which the missile leaves and returns to the water.
78. ## Physics

An object moving with uniform acceleration has a velocity of 13.0 cm/s in the positive x-direction when its x-coordinate is 2.73 cm. If its x-coordinate 2.95 s later is −5.00 cm, what is its acceleration? cm/s^2 Express the position of the object in
79. ## Dynamics

The acceleration of a perticle as it moves along a straight line is geven by a=(2t-1) m/s2. If x=1m and v=2m/s when t=0s, determine the particle's velocity and position when t=6s. Also, determine the total distance the particle travels during this time
80. ## Math

an object is moving along the x-axis such that the position of the object in masters at time t in seconds is giving by the function x(t)=t^3-12t^2+36t-5, for 0<=t<=8 a- when is the object moving right? and when to the left? b- When is the object's
81. ## calculus

Suppose the following about a certain object: I. The object's altitude is a function of time, represented by the function A(x) where here x is time. II. The temperature of the object is a function of its velocity, represented by the function T(x), where
82. ## precalc

An object is attached to a coiled spring. The object is pulled down (from its rest position) and then released. Given that the distance from its rest position at time t = 0 is 3 inches, its amplitude is 3 inches, and its period is 1.5 seconds, write an
83. ## Calculus the derivative

Can you please check my answers and help me fix the one I don't or or did wron . The height in feet of a free falling object t seconds after release is s(t)=-16t^2+ v_0t+s_0, where s_0 is the height(in feet) at which the object is realsed, and v_0 is the
84. ## Dynamics

A particle is attached to point O from A by the force F=-k/x3. If x=x0 and v=0 when t=0, determine velocity and acceleration as a function of x, and the time it takes to travel from A to O.
85. ## Physics

A hot-air balloon is rising vertically at a speed of 10 m s–1. An object is released from the balloon. The graph shows how the velocity of the object varies with time from when it leaves the balloon to when it reaches the ground four seconds later. It is
86. ## Calculus

Use the position function s(t)=-4.9t^2+ 150, which gives the height (in meters) of an object that has fallen from 150 meters. Teh velocity at time t=a seconds is given by: lim as t approaches a s(a)-s(t) divided by a-t a) find the velocity of the object
87. ## physics

A race car moves such that its position fits the relationship x = (5.0 m/s)t + (0.75 m/s3)t3 where x is measured in meters and t in seconds. (a) Plot a graph of the car s position versus time. (b) Determine the instantaneous velocity of the car at t = 4.0
88. ## Physics

A race car moves such that its position fits the relationship x = (5.0 m/s)t + (0.75 m/s3)t3 where x is measured in meters and t in seconds. (a) Plot a graph of the car s position versus time. (b) Determine the instantaneous velocity of the car at t = 4.0
89. ## physics!!

The figure below shows the acceleration as a function of time for an object. (a) If the object starts from rest at t = 0, what is the velocity of the object as a function of time? for 0s < t < 10s v(t) = m/s for 10s < t < 26s v(t) = m/s (b) If
90. ## physics!!

The figure below shows the acceleration as a function of time for an object. (a) If the object starts from rest at t = 0, what is the velocity of the object as a function of time? for 0s < t < 10s v(t) = m/s for 10s < t < 26s v(t) = m/s (b) If
91. ## Physics

suppose that you wish to determine how far away from your position lightning has struck. the thunder that results from lightning expands outward in all directions at a constant speed (you may assume 343 m/s at 20C). when counting seconds between the time
92. ## physics

. A race car moves such that its position fits the relationship x = (5.0 m/s)t + (0.75 m/s3)t3 where x is measured in meters and in t in seconds. (a) Plot a graph of the car’s position versus time. (b) Determine the instantaneous velocity of the car at
93. ## math

Experimentally it is found that a 6 kg weight stretches a certain spring 6 cm. If the weight is pulled 4 cm below the equilibrium position and released: a. Set up the differential equation and associated conditions describing the motion. b. Find the
94. ## calculus

the vector function r(t)=< 5 sin t, 3 sec t > , represents the position of a particle at time t. find the velocity v (t) and acceleration a (t). I don't know how to solve it without the t given. Please help
95. ## Physics

An object at rest accelerates through a distance of 1.5 m at which point the instantaneous velocity of the object is 3.5m/s. Determine: a. The average acceleration of the object b. The time it took the object to travel 1.5m c. The average velocity of the
96. ## Physics

The coordinate of a boy running across a parking lot as a function of time is gives as :x0†3=3t*2 7.2t 28 and y0†3=0.28t*2 - 9.1t 30...express the boys position vector r0†3 and velocity v0†3 in unit vector rotation and find the magnitude
97. ## calculus

A flea moves along the line y = -3 according to the equation: x = t^3 - 9t^2 + 24t where x is its x coordinate at time t secs. Determine: 1) the position, velocity, and acceleration of the flea at time 3 secs. Answer: position - 3^3 - 9(3)^2 + 24(3) = 18
98. ## trigonometry

An object is attached by a string to the end of a spring. When the weight is released it starts oscillating vertically in a periodic way that can be modeled by a trigonometric function. The object's average height is −20 cm (measured from the top of
99. ## Physics

An object at rest accelerates through a distance of 1.5 m at which point the instantaneous velocity of the object is 3.5m/s. Determine: a. The average acceleration of the object b. The time it took the object to travel 1.5m c. The average velocity of the
100. ## Physics

Consider a particle undergoing positive acceleration. (1) what is the shape of the position-time graph? (2) How do we determine an instantaneous velocity from the position-time graph?