Question

A $50$kg sprinter, starting from rest, runs $50$m in $7.0$s at constant acceleration.

a. What is the magnitude of the horizontal force acting on the sprinter?

b. What is the sprinter’s power output at $2.0$s, $4.0$s, and$6.0$ s?

Short answer

a). Horizontal force is 102.04 N

b). Out power at t=2 s is 416.32 W, at t=4 s is 832.64 W and at t=6 s is 1284.96 W

Step-by-step solution

Step 1. Given Information

We have,

Mass $m=50$kg

$s=50$m in $7.0$ s at constant acceleration

Step 2. Find the acceleration

Magnitude of force can be found second Newton's law $F=ma$

Acceleration of sprinter can be found form equation from kinematics that connects distance, time and constant acceleration

$$\begin{gathered} s=\frac{1}{2}a{t}^2 \\ \Rightarrow a=\frac{2s}{t^2} \\ a=\frac{2·50m}{{(7s)}^2} \\ a=2.04m/s^2 \end{gathered}$$

Step 3. Part a). Find the magnitude of force

So,

$$\begin{gathered} F=ma \\ F=50kg·2.04m/s^2 \\ F=102.04N \end{gathered}$$

Part b). Find the sprinter output power

Output power can be found from $P=Fv$

$$\begin{gathered} P_{t=2s}=102.04N·2.04m/s^2·2s=416.32W \\ {P}_{t=4s}=102.04N·2.04m/s^2·6s=832.64W \\ {P}_{t=6s}=102.04N·2.04m/s^2·6s=1248.96W \end{gathered}$$