Final answer:
The kinetic energy of the car increases by a factor of 4.
Step-by-step explanation:
The kinetic energy of an object is given by the formula:
KE = 1/2 * mass * velocity^2
So, to find the ratio of the kinetic energy when the velocity increases from 10 m/s to 20 m/s, we can use the formula:
Ratio = (KE final / KE initial)
Substituting the velocities, the ratio of the kinetic energy is:
Ratio = (1/2 * mass * (20 m/s)^2) / (1/2 * mass * (10 m/s)^2)
This simplifies to:
Ratio = (20^2) / (10^2)
Ratio = 4
Therefore, the kinetic energy increases by a factor of 4.