Question

If the speed of the car is halved, how does the kinetic energy change?

Answer 1

Step 1: Given data

Let the initial speed of the car be $=v$

So, the new speed of the car, $v\text{'}=\frac{v}{2}$

Let $m$ be the mass of the car.

Step 2: Calculation of final kinetic energy

The initial kinetic energy is given by, $K=\frac{1}{2}\times m\times v^2$

If the velocity is halved, then we can write the final kinetic energy as:

$K\text{'}=\frac{1}{2}mv{\text{'}}^2$

$$\begin{gathered} K\text{'}=\frac{1}{2}\times m\times {\left(\frac{v}{2}\right)}^2 \\ K\text{'}=\frac{1}{2}\times m\times {\frac{v}{4}}^2 \\ K\text{'}=\frac{1}{4}\times K \end{gathered}$$

Thus, if the velocity is halved, the kinetic energy will decrease to 1/4^th of its original value.