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Question
A car of mass 120 kg is moving at a speed 18 km/h and it accelerates to attain a speed of 54 km/h in 5 seconds. Calculate:
- the work done by the engine.
- the power of the engine.
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Solution 1
a. By work energy theorem
Work done = Change in K.E. of body
= `1/2"m"("v"^2-"u"^2)`
= `1/2xx120[(15)^2-(5)^2]`
= `1/2xx120[200]`
= 12000 J
b. Power of engine = `"Work done"/"Time"`
= `12000/5`
= 2400 W
Solution 2
(a) Given,
Initial velocity (vi) = 18 km/h
Converting km/h to m/s
`18xx5/18 = 5` m/s
Final velocity (vf) = 54 km/h
Converting km/h to m/s
`54xx5/18 = 15` m/s
Work done = Change in kinetic energy = `1/2 m (v_f^2 - v_i^2)`
`1/2 xx120xx(15^2-5^2)`
`1/2xx120xx(225-25)`
= 60 × 200 = 12000 J
Hence, work done = 12000J
(b) Power = `"work done"/"time" = 12000/5`
= 2400 watt
Hence, power of engine = 2400 watt.
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