If a moving car speeds up until it is going twice as fast, how much kinetic energy doe s it have compared with its initial kinetic enegy

The kinetic energy of an object of mass m and velocity v is given by


Let's call  the initial speed of the car, so that its initial kinetic energy is

where m is the mass of the car. 

The problem says that the car speeds up until its velocity is twice the original one, so 

and by using the new velocity we can calculate the final kinetic energy of the car

so, if the velocity of the car is doubled, the new kinetic energy is 4 times the initial kinetic energy.

Dformation of a precipitate