Question

1. for how long should a force of 130 n be applied to an object of mass 50 kg to change its speed from 20 m/s to 60 m/s?

a. 0.031 s
b. 0.065 s
c. 15.4 s

Explanation:

Step1: Use the impulse - momentum theorem

The impulse - momentum theorem states that \(F\Delta t = m\Delta v\), where \(F\) is the force, \(\Delta t\) is the time interval, \(m\) is the mass, and \(\Delta v=v - u\) ( \(v\) is the final velocity and \(u\) is the initial velocity).
Given \(F = 130\space N\), \(m = 50\space kg\), \(u = 20\space m/s\), \(v = 60\space m/s\). First, calculate \(\Delta v\):
\(\Delta v=v - u=60 - 20=40\space m/s\)

Step2: Solve for \(\Delta t\)

From \(F\Delta t=m\Delta v\), we can express \(\Delta t\) as \(\Delta t=\frac{m\Delta v}{F}\)
Substitute the values: \(\Delta t=\frac{50\times40}{130}=\frac{2000}{130}\approx15.4\space s\)

Answer:

C. \(15.4\space s\)