Instantaneous Velocity Car Problem

[mopar969]

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 = 2.40m/s^2 and c = 0.120 m/s^3. How do you calculate the average velocity of the car for the time interval t=0 to t=10.

I think that maybe I need to take the derivative of the equation but then what please help!

 

[collinsmark]

Hello mopar969,

How do you calculate the average velocity of the car for the time interval t=0 to t=10.

If you only need to find the average velocity, simply calculate the total distance traveled, divided by the time it takes to get there.

 

[mopar969]

Thank you. I can't believe that it was that simple. I was thinking instantaneous velocity that is why I was thinking about taking its derivative.
However, the question has another part to it that I am stuck on it says:

How long after stating from rest is the car again at rest? Please Help and Thanks.

 

[Johnny Blade]

You're searching the time t when the velocity is 0.

x(t)= bt^2 -ct^3, this finds the displacement as a function of time. You'll need another equation (related to this one) to find the velocity as a function of time.

 

[mopar969]

Would I need the derivative of the displacement function?

 

[Johnny Blade]

Yes that would give you the velocity.

 

[mopar969]

My next problem is how do I get t by itself?

 

[mopar969]

Never mind I realized that I could use the quadratic formula.