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: Calculate the acceleration

According to Newton's second law \(F = ma\), where \(F\) is the force, \(m\) is the mass, and \(a\) is the acceleration.
We can find \(a=\frac{F}{m}\). Substituting \(F = 85\space N\) and \(m=175\space kg\), we get \(a=\frac{85}{175}\space m/s^{2}\approx0.486\space m/s^{2}\).

Step2: Use the kinematic equation \(v = u+at\)

Here, \(v\) is the final velocity (\(v = 30\space m/s\)), \(u\) is the initial velocity (which we want to find), \(a\) is the acceleration (\(a=\frac{85}{175}\space m/s^{2}\)), and \(t\) is the time (\(t = 12\space s\)).
Rearrange the equation for \(u\): \(u=v - at\).
Substitute the values: \(u = 30-\frac{85}{175}\times12\).
First calculate \(\frac{85\times12}{175}=\frac{1020}{175}\approx5.83\).
Then \(u=30 - 5.83=24.17\space m/s\)

Answer:

\(24.17\space m/s\)