Question

a sled with mass 50 kg has a starting velocity of 8 m/s. it exerts a force of 15 n in a time interval of 4 s. what is the sleds final velocity? 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 acceleration using \(F = ma\)

Given \(F = 15N\), \(m = 50kg\). From \(F=ma\), we can find \(a=\frac{F}{m}\). So \(a=\frac{15}{50}= 0.3m/s^{2}\)

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

Given \(u = 8m/s\), \(a = 0.3m/s^{2}\), \(t = 4s\). Substitute into \(v=u + at\). Then \(v=8+0.3\times4\)
\(v=8 + 1.2\)

Step1: Calculate acceleration using \(F = ma\)

Given \(F = 85N\), \(m = 175kg\). From \(F = ma\), we get \(a=\frac{F}{m}\). So \(a=\frac{85}{175}\approx0.486m/s^{2}\)

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

Given \(v = 30m/s\), \(a\approx0.486m/s^{2}\), \(t = 12s\). Rearrange \(v=u + at\) to \(u=v - at\). Then \(u=30-0.486\times12\)
\(u=30-5.832\)

Answer:

\(9.2m/s\)

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