Car at traffic light with position x(t) = bt² + ct³

[jcz2]

Physics homework problem...please help!

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) = b*t^2 + c*t^3, where b= 2.60 and c= 0.110 .

Homework Equations

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

The Attempt at a Solution

i made the x(t) = 0 and i solved for t, and i got t = 0 and t = 23.6364, but when i put in t = 23.6364 in the solution it was wrong..can someone please help me...did i do this wrong?

 

[berkeman]

From a quick look, the distance seems to be increasing monotonically. What am I missing?

 

[S_Happens]

First off, answer me this. When you set x(t) to zero, what exactly is it that you're setting to zero. Hint: Is it velocity that you're setting to zero?

Second, are you taking or have you taken basic calculus? If not then you are probably leaving out some information. If so, then do you know of any relationship between position and velocity?

P.S.- Technically if you solved that equation, you had to get zero (twice) and a negative 23.XXX, but it doesn't do much good to solve a (seemingly) position equation first (and only) when you need to start with velocity.