A dynamics cart released from rest at the top of an inclined plane of length 2l reaches the bottom with acceleration a_1 and velocity v. When length is reduced to l, it reaches bottom with acceleration a_2 and same velocity v. What is the ratio a_1 / a_2?

1. Step: a = v^2 / (2s). 2. Step: a_1 = v^2 / (4l), a_2 = v^2 / (2l). 3. Step: a_1 / a_2 = 1/2.