Question

A car traveling at 60 mph has how much more energy than a car going at 20 mph? How many times does the kinetic energy of a car increase when traveling 60 mph as opposed to traveling 30 mph? K.E. increases _____ times.

Answer 1

Explanation :

(a) Initial velocity, v₁ = 60 mph

Final velocity, v₂ = 20 mph

Let KE₁ and KE₂ are the initial and final kinetic energies.

`(KE_1)/(KE_2)=(1/2mv_1^2)/(1/2mv_2^2)`

`(KE_1)/(KE_2)=((60)^2)/((20)^2)`

`(KE_1)/(KE_2)=9`

So, the kinetic energy increases 9 times.

(b) Initial velocity, v₁ = 60 mph

Final velocity, v₂ = 30 mph

Let KE₁ and KE₂ are the initial and final kinetic energies.

`(KE_1)/(KE_2)=(1/2mv_1^2)/(1/2mv_2^2)`

`(KE_1)/(KE_2)=((60)^2)/((30)^2)`

`(KE_1)/(KE_2)=4`

So, the kinetic energy increases 4 times.

Hence, this is the required solution.