Question

What is the magnitude of the acceleration of a sprinter running at10 m/s when rounding a turn of radius 25 m?

Short answer

The magnitude of the acceleration$a=4.00\mathrm{m}/{\mathrm{s}}^2$

Step-by-step solution

Given data

The speed of the sprinter is v = 10 m/ s

The radius of the turn is r = 25 m

Understanding the concept

The sprinter is rounding a turn hence it has centripetal acceleration. Use the formula for the centripetal acceleration in terms of velocity and radius to calculate the acceleration.

Formulae:

The centripetal acceleration is $a=\frac{v^2}{r}$.

Calculate the magnitude of the acceleration of the sprinter

The sprinter is rounding a turn; hence it has centripetal acceleration. The centripetal acceleration of the sprinter is

$$\begin{gathered} \mathrm{a}=\frac{{\mathrm{v}}^2}{\mathrm{r}} \\ =\frac{{(10\mathrm{m}/\mathrm{s})}^2}{25\mathrm{m}} \\ =4.00\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

Therefore, the magnitude of the acceleration of the sprinter is $4.00\mathrm{m}/{\mathrm{s}}^2$.