A half-kilogram ball is thrown vertically upward at a speed of 25 meters per second (m/s). Its velocity v(t) (in m/s) at time t (in seconds), is given by v(t) = 25 - 9.8t. Its kinetic energy K(v) (in Joules) is given by K(v) = 0.5v2. Express the ball's kinetic energy as a function of time.
I think I just need to plug v(t) in for "v" in K(v), to get K in terms of t:
K(v(t)) = 0.5[25 - 9.8t]2
= 0.5[625 - 490t + 96.04t2]
=312.5 - 245t + 48.0t2
Am I missing anything, or is it really this easy? Thank you.