A car is stopped at a traffic light. It then travels along a straight road so th

Question

A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x(t) = bt^2 - ct^3, where b = 3.00 m/s^2 and c = 0.130 m/S^3. Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 S. Calculate the instantaneous velocity of the car at t = 0. Calculate the instantaneous velocity of the car at t = 5.00 s. Calculate the instantaneous velocity of the car at t = 10.0 S. How long after starting from rest is the car again at rest?

Explanation / Answer

Here,

x = b * t^2 - ct^3

x = 3 t^2 - 0.130 * t^3

part A) for the average velocity

average velocity = (x(10) - x(0))/10

average velocity = (3 * 10^2 - 0.130 * 10^3)/10

average velocity = 17 m/s

part B)

velocity , v = dx/dt

v = d/dt(3 t^2 - 0.130 * t^3)

v = 6 * t - 0.390 * t^2

at t = 0 s

v = 0 m/s

the instantenous velocity at t = 0 s is 0 m/s

part C)

at t = 5 s

v = 6 * t - 0.390 * t^2

v = 6 * 5 - 0.390 * 5^2

v = 20.25 m/s

the instantenous velocity at t = 5 s is 20.25 m/s

part D)

at t = 10 s

v = 6 * t - 0.390 * t^2

v = 6 * 10 - 0.390 * 10^2

v = 21 m/s

the instantenous velocity at t = 5 s is 21 m/s

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