Question

One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 7 m/s, they then have the same energy. What were the original speeds of the two cars?

Answer 1

We have

and

Now, the velocities are increased by 7 m/s. The new velocities become

Now, the kinetic energy becomes equal. i.e

and

So, the velocity of the first car is 4.95 m/s and the velocity of the second car is 9.90 m/s.