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June 2014 p41 q1
3459
A train is moving at constant speed \(V \text{ m s}^{-1}\) along a horizontal straight track. Given that the power of the train’s engine is 1330 kW and the total resistance to the train’s motion is 28 kN, find the value of \(V\).
Solution
The power \(P\) of the train is given by the formula:
\(P = F \times V\)
where \(F\) is the force (resistance) and \(V\) is the speed.
Given:
\(P = 1330 \text{ kW} = 1330000 \text{ W}\)
\(F = 28 \text{ kN} = 28000 \text{ N}\)
Substitute these values into the formula:
\(1330000 = 28000 \times V\)
Solve for \(V\):
\(V = \frac{1330000}{28000} = 47.5 \text{ m s}^{-1}\)