Question

A motorcar of mass 1200 kg is moving along a straight line
with a uniform velocity of 90 km/h. Its velocity is slowed down
to 18 km/h in 4 s by an unbalanced external force. Calculate
the acceleration and change in momentum. Also calculate the
magnitude of the force required.

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Answer 1

Step-by-step explanation:

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$\displaystyle \sf \: \longrightarrow \: mass \: of \: car \: = \: 1200kg \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \: \longrightarrow \: initial \: velocity \: = \: 90 \frac{km}{h} = \: 25 \frac{m}{s} \\ \\ \displaystyle \sf \: \longrightarrow \: final \: velocity \: = 18 \frac{km}{h} = 5 \frac{m}{s} \: \: \: \: \: \: \\ \\ \displaystyle \sf \: \longrightarrow \: time \: taken \: = 4s \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \: \longrightarrow \: first \: law \: of \: motion \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \: \longrightarrow \: v \: = u + at \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \: \longrightarrow \: 5 = 25 + a(4) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \: \longrightarrow \: a \: = \: - 5 \frac{m}{s} (velocity \: is \: decreases) \\ \\ \\ \\ \\ \\ \displaystyle \sf \: \longrightarrow \: momentum \: = \: m(v - u) \\ \\ \displaystyle \sf \: \longrightarrow \: momentum = \: 1200(5 - 25) \\ \\ \displaystyle \sf \: \longrightarrow \: 24000kg \frac{m}{s}$