A car is traveling at 15 m/s

1) How fast would the car need to go to double its kinetic energy?

Kinetic Energy(KE) = 1/2 m V²
The first part (1/2 m) doesn’t change, you need a new value for V such that

V(new)² = 2 x V(old)²
V(new) = (2 x 15²)  ^1/2
V(new) = 450^1/2
which is approx. = 21.21 meters per second.

 

2) By what factor does the car’s kinetic energy increase if its speed is doubled to 30 m/s?

When the velocity is doubled, the kinetic energy is four times because in the way we compute kinetic energy is by taking the square of the velocity. 2v² = 4v²
=4 times