Question

a snowmobile with mass 175 kg exerts a force of 85 n in 12 s. the final velocity that it reaches is 30 m/s. what was the snowmobiles initial velocity?

Explanation:

Step1: Use the impulse - momentum theorem

The impulse - momentum theorem is \(J = \Delta p\), where \(J = F\Delta t\) (impulse) and \(\Delta p=m(v - u)\) (change in momentum). So \(F\Delta t=m(v - u)\).

Step2: Rearrange the formula to solve for the initial velocity \(u\)

We have \(F\Delta t=m(v - u)\). First, expand it: \(F\Delta t=mv - mu\). Then, \(mu = mv - F\Delta t\). So \(u=\frac{mv - F\Delta t}{m}\).
Substitute \(m = 175\space kg\), \(F = 85\space N\), \(\Delta t=12\space s\), \(v = 30\space m/s\) into the formula:

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Answer:

The initial velocity of the snowmobile is \(24.17\space m/s\)