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:

1. the work done by the engine.
2. the power of the engine.

Answer 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

Answer 2

(a) Given,

Initial velocity (v_i) = 18 km/h

Converting km/h to m/s

`18xx5/18 = 5` m/s

Final velocity (v_f) = 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.