Find the minimum acceleration required to avoid a collision (minimum deceleration).

Given the initial velocity of a car approaching a traffic jam and given the distance to the nearest stopped car, we find the minimum acceleration required to avoid a collision. We could also call this the minimum deceleration.

We are asked for the magnitude of this minimum acceleration, meaning we'll just ignore the minus sign on the acceleration for this problem. The key physical point in this problem is that we want the velocity to go to zero precisely when the car arrives at the stationary car 225m away. So we have a final velocity of zero, a known final position of 225m and we're given the initial velocity of the car. Plugging in to the time-independent kinematics equation v^2=v_0^2+2a(x-x_0), we solve for the acceleration. The acceleration is negative because it points to the left, so we erase the minus sign to state the minimum magnitude of the acceleration.

Next we compute the time for the car to stop at this minimum acceleration. We use our second kinematics equation describing the velocity as a function of time: v=v_0+at. Since we know the initial and final velocity and we know the acceleration, t is the only unknown here and we quickly solve for the deceleration time to avoid a collision.