When Does the Car Come to Rest Again?

[MellowOne]

Homework Statement

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 = 2.30 m/s^2 and c = 0.120 m/s^3.

How long after starting from rest is the car again at rest?

Homework Equations

dx/dt

The Attempt at a Solution

The problem I'm having with this question is I can't figure out how you can find the deceleration after the car stops accelerating. I know at t = 0 the velocity is 0 m/s, at t = 5s the velocity is 14m/s, and at t = 10s, the velocity is 10m/s this means the car decelerated from t = 5s to t = 10s. How do I find the deceleration to find how long it took the car to reach maximum velocity assuming it's 14.0m/s to come back to rest?

 

[w3390]

Try using the fact that a=(delta v)/(delta t)

 

[MellowOne]

Ok, I got it...I just took the derivative of the distance formula which would make it into the velocity formula. Then I set the velocity equal to 0 and used the quadratic equation to find t.

 

[w3390]

Sounds right