Chapter 4, Problem 550RE

A rocket is launched into space; its kinetic energy is given by $K\left(t\right)=\left(\frac{1}{2}\right)m\left(t\right)v{\left(t\right)}^2$ , where K is the kinetic energy in joules, m is the mass of the rocket in kilograms, and v is the velocity of the rocket in meters/second. Assume the velocity is increasing at a rate of 15 m/sec²and the mass is decreasing at a rate of 10 kg/sec because the fuel is being burned. At what rate is the rocket’s kinetic energy changing when the mass is 2000 kg and the velocity is 5000 m/sec? Give your answer in mega-Joules (MJ), which is equivalent to 10⁶ J.