Question

a sports car accelerates from rest to 27 m/s in 6.3 seconds. the car exerts a force of 4106 n. what is the mass of the car?

Explanation:

Step1: Calculate acceleration

Use the formula \(a=\frac{v - u}{t}\), where \(u = 0\space m/s\) (starts from rest), \(v=27\space m/s\), and \(t = 6.3\space s\).
\(a=\frac{27- 0}{6.3}=\frac{27}{6.3}\space m/s^{2}\)

Step2: Use Newton's second law \(F = ma\)

Rearrange for \(m\), \(m=\frac{F}{a}\). Given \(F = 4106\space N\) and \(a=\frac{27}{6.3}\space m/s^{2}\)
\(m=\frac{4106}{\frac{27}{6.3}}=4106\times\frac{6.3}{27}\)
\(m=\frac{4106\times6.3}{27}=\frac{25867.8}{27}=958.066\cdots\approx958\space kg\)

Answer:

\(958\space kg\)