VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Kinetic energy, in the first case, is one-half m v 1 squared and, in the second case, after the kinetic energy increases, it's gonna be one-half m v 2 squared. We are told in the second case, the kinetic energy is 3 times it was in the first case. So we write, one-half m v 2 squared, in place of k E 2, and that equals 3 times k E 1, which we will write here in red. And we see that the m's cancel and the one-halves cancel and we have, v 2 squared equals 3 times v 1 squared, which means v 2 equals square root 3 v 1 when you take the square root of both sides. So v 2 has increased by a factor of root 3 times v 1. When you have this speed, becoming half what it was in the second case, we are gonna see how the kinetic energy changes. So we have kinetic energy, in the second case, is one-half m v 2 squared but where v 2 is replaced by v 1 over 2; this 2 in the denominator becomes squared so it becomes one-quarter and then I wrote the rest of it in brackets here; one-half m v 1 squared so we can see that this is k E 1. So k E 2 is a quarter of k E 1. Kinetic energy decreases, or is multiplied by a factor of one-quarter when the speed is reduced by a half.