Question

a racecar increases its speed from 35 m/s to 45 m/s in 10 s. it has a mass of 500 kg. what force did it use to do this?
a runner with a mass of 60 kg exerts a force of 30 n to increase her speed from 5 m/s to 8 m/s. how long did it take her to do this?

Explanation:

Step1: Find acceleration for racecar

Using the formula \(a=\frac{v - u}{t}\), where \(u = 35\ m/s\), \(v=45\ m/s\), \(t = 10\ s\).
\(a=\frac{45 - 35}{10}=\frac{10}{10}=1\ m/s^{2}\)

Step2: Calculate force for racecar

Using Newton's second law \(F = ma\), with \(m = 500\ kg\), \(a = 1\ m/s^{2}\)
\(F=500\times1 = 500\ N\)

Step3: Find acceleration for runner

Using Newton's second law \(a=\frac{F}{m}\), with \(F = 30\ N\), \(m = 60\ kg\)
\(a=\frac{30}{60}=0.5\ m/s^{2}\)

Step4: Calculate time for runner

Using the formula \(a=\frac{v - u}{t}\), rearranged to \(t=\frac{v - u}{a}\), with \(u = 5\ m/s\), \(v = 8\ m/s\), \(a=0.5\ m/s^{2}\)
\(t=\frac{8 - 5}{0.5}=\frac{3}{0.5}=6\ s\)

Answer:

The force used by the racecar is \(500\ N\). The time taken by the runner is \(6\ s\).