Question

If you triple the speed from 20km/h to 60km/h, by what factor does the KE increase?

Answer 1

The kinetic energy increases by a factor of 9

Step-by-step explanation:

Kinetic Energy

It's the energy related to the speed of an object and is calculated by the formula

`\displaystyle K=(mv^2)/(2)`

Let's suppose the initial speed of the mass is
`v_o`, then the kinetic energy is

`\displaystyle K_o=(mv_o^2)/(2)`

Now the speed will triple, i.e.
`v_1=3v_o`. The new kinetic energy is

`\displaystyle K_1=(mv_1^2)/(2)`

`\displaystyle K_1=(m(3v_o)^2)/(2)`

`\displaystyle K_1=9(mv_o^2)/(2)`

Thus

`K_1=9K_o`

The kinetic energy increases by a factor of 9

Let's check with numbers:
`v_o=20,\ v_1=60`

`\displaystyle K_o=(m20^2)/(2)=200m`

`\displaystyle K_1=(m60^2)/(2)=1800m`

The relation is

`\displaystyle (K_1)/(K_o)=9`

The new kinetic energy is nine times the initial kinetic energy.