Question

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

Answer 1

Answer:

The kinetic energy increases by a factor of 9

Explanation:

Kinetic Energy

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

$\displaystyle K=\frac{mv^2}{2}$

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

$\displaystyle K_o=\frac{mv_o^2}{2}$

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

$\displaystyle K_1=\frac{mv_1^2}{2}$

$\displaystyle K_1=\frac{m(3v_o)^2}{2}$

$\displaystyle K_1=9\frac{mv_o^2}{2}$

Thus

$K_1=9K_o$

The kinetic energy increases by a factor of 9

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

$\displaystyle K_o=\frac{m20^2}{2}=200m$

$\displaystyle K_1=\frac{m60^2}{2}=1800m$

The relation is

$\displaystyle \frac{K_1}{K_o}=9$

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