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)=bt2?ct3, where b = 2.40m/s2 and c = 0.120m/s3 . A) calculate the average velocity of the car for the time interval t=0 to t= 10 B) calculate the instantaneous velocity of the car at t=5 s C) calculate the instantaneous velocity of the car at t= 10 s D) how long after from rest is the car again at rest? 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)=bt2?ct3, where b = 2.40m/s2 and c = 0.120m/s3 . A) calculate the average velocity of the car for the time interval t=0 to t= 10 B) calculate the instantaneous velocity of the car at t=5 s C) calculate the instantaneous velocity of the car at t= 10 s D) how long after from rest is the car again at rest? 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)=bt2?ct3, where b = 2.40m/s2 and c = 0.120m/s3 . 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)=bt2?ct3, where b = 2.40m/s2 and c = 0.120m/s3 . 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)=bt2?ct3, where b = 2.40m/s2 and c = 0.120m/s3 . A) calculate the average velocity of the car for the time interval t=0 to t= 10 B) calculate the instantaneous velocity of the car at t=5 s C) calculate the instantaneous velocity of the car at t= 10 s D) how long after from rest is the car again at rest? A) calculate the average velocity of the car for the time interval t=0 to t= 10 B) calculate the instantaneous velocity of the car at t=5 s C) calculate the instantaneous velocity of the car at t= 10 s D) how long after from rest is the car again at rest?

Explanation / Answer

x(t) = 2.4*t^2 - 0.120*t^3
v(t) = x'(t) = 4.8*t - 0.360*t^2

v(5) =4.8*5 - 0.360*5^2 = 24m/s
v(10) = 4.8*10 - 0.360*10^2 = 48 m/s

How long til it comes back to rest:
set v(t) = 0 and solve for t
0 = 4.8*t - 0.360t^2
0 = t*(4.8-0.360*t)
4.8-0.360*t = 0
t = 13.33 s

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