Question

You are a participant in a demolition derby. The damage that you do to the other cars depends on your kinetic energy. If you quintupled your car's speed, how many times more kinetic energy is contained in the car's motion? What does more to increase your kinetic energy and therefore your ability to destroy the other cars, doubling your speed or tripling the mass of your What happens to the kinetic energy of your car when you crash into another car?

Answer 1

Kinetic Energy = 1/2 * mv^2

(a)
If we Increase the speed of Car 5 times.

The kinetic Energy = 1/2 * m(5v)^2
K.E = 1/2 * mv^2 * 25
K.Enew = 25 * K.Eold
So Kinetic Energy will increase 25 fold.

(b)

If we do double the speed,
K.E = 1/2 * m (2v)^2
K.E = 4 * 1/2 * mv^2

i.e Kinetic Energy will be 4 times the old K.E.
If we triple the mass, KInetic Energy will be 3 times the old K.E.

So, Doubling the Speed will be better.

(c)
Kinetic Energy will be lost into some other form of energy which can be Thermal Energy, Sound , Or the other object will gain some Kinetic Energy due to the crash.