Question

How many times does the kinetic energy of a car increase when traveling 60 mph as opposed to traveling 30 mph? K.E. increases

Answer 1

So basically the Kinetic Energy increases 4 times

Answer 2

The answer to the question is 4 times i.e the kinetic energy of the car will increase four times when it will move with 60 mph as opposed to travelling with 30 mph.

CALCULATION:

Let us a consider a body having mass m which is moving with a velocity v.

The kinetic energy of the body is calculated as -

Kinetic energy K.E =
`(1)/(2)mv^2`

Let us consider the initial and final velocity of the car are denoted as
`v_(1)\ and\ v_(2)`.

Here,
`v_(1)=\ 30 mph`

`v_(2)=\ 60\ mph`

The initial kinetic energy of the car
`K.E_(1)=\ (1)/(2)mv_(1)^2`

The final kinetic energy of the car
`K.E_(2)=\ (1)/(2)mv_(2)^2`

Hence, the ratio of final kinetic energy to initial kinetic energy is calculated as -

`\frac{K.E_(2)} {K.E_(1)} =\ \frac{1/2mv_(2)^2} {1/2mv_(1)^2}`

`\frac{K.E_(2)} {K.E_(1)}=\ \frac{v_(2)^2} {v_(1)^2}`

`=\ ((60)^2)/((30)^2)`

`=\ (4)/(1)`

Hence, the kinetic energy of the car will be increased to 4 times when it will move with speed from 30 mph to 60 mph.