Question

Two cars are moving. The first car has thrice the mass of the second car but only 1/3 as the 

kinetic energy. When both cars increase their speed by 9 m/s, they then have the same kinetic 

energy. 

Calculate the original speeds of the first car.

Answer 1

$$M=3m\\0.5Mv^2=0.5\frac{1}{3}mV^2\\3v^2=\frac{1}{3}V^2\\V=3v$$

$$0.5M(v+9)^2=0.5m(V+9)^2\\3(v+9)^2=(3v+9)^2\\v=5.2\frac{m}{s}\\V=15.6\frac{m}{s}$$