A car with a mass of 1000 kg crashes into a rubber wall with an initial velocity of 30 m/s and recoils at 15 m/s. The change in momentum occurs over 1 meter. Find the force that the car experiences and time for which this force acts.
v22 - v12=2ad
The Attempt at a Solution
I started by plugging into the first equation and got:
(-15)2 - 302= 2(a)(1)
Solving gives an acceleration of -387.5 m/s^2, but I was thinking about this and there is a problem. As the recoil velocity approaches the magnitude of the initial velocity (e.g., 30 -> -30), the left-hand side of the first equation approaches zero. How can I account for the fact that the velocities are in different directions, meaning that the acceleration should be even larger?