The kinetic energy of an object of mass m and velocity v is given by
[tex]K= \frac{1}{2} mv^2 [/tex]
Let's call [tex]v_i[/tex] the initial speed of the car, so that its initial kinetic energy is
[tex]K_i = \frac{1}{2} mv_i^2[/tex]
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
[tex]v_f = 2 v_i[/tex]
and by using the new velocity we can calculate the final kinetic energy of the car
[tex]K_f = \frac{1}{2} mv_f^2 = \frac{1}{2}m (2 v_i)^2 = 4 ( \frac{1}{2} mv_i^2)=4 K_i [/tex]
so, if the velocity of the car is doubled, the new kinetic energy is 4 times the initial kinetic energy.
