Chapter 9, Problem 1CQ

If a particle’s speed increases by a factor of 3, by what factor does its kinetic energy change?

To determine

The factor by which the KE of a particle change if the speed of the particle increases by a factor of 3.

Answer to Problem 1CQ

Solution:

The KE increases by a factor of 9.

Explanation of Solution

Given Info:

The speed of a particle increases by a factor of 3.

Formula used:

The KE of a body of mass $m$ moving with speed $v$ is $\frac{1}{2}m{v}^2$.

Calculation:

When the speed increases by a factor of 3, the new KE is

${\text{KE}}_{\text{new}}=\frac{1}{2}m{\left(3v\right)}^2=9\left(\frac{1}{2}m{v}^2\right)=9{\text{KE}}_{\text{old}}$

Conclusion:

The KE of particle is directly proportional to the square of its speed.