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.
Topic: Work-energy theorem
Answer
Given: m = 120 kg, u = 18 km/h, v = 54 km/h, t = 5 s
Convert the speeds to metres per second (multiply by 5/18): u = 18 × 5/18 = 5 m s⁻¹ v = 54 × 5/18 = 15 m s⁻¹
The work done by the engine equals the gain in kinetic energy: W = ½ m v² − ½ m u² = ½ m (v² − u²) = ½ × 120 × (15² − 5²) = 60 × (225 − 25) = 60 × 200 = 12 000 J
Work done by the engine = 12 000 J (12 kJ)
Convert km/h to m/s before anything else, by multiplying by 5/18. Working in km/h gives a number that is not in joules at all.
Take the difference of the SQUARES, not the square of the difference. Here 15² − 5² = 200; (15 − 5)² would be 100, giving half the right answer. They are not the same thing, and this is the most common error in work-energy questions.
The 5 seconds is not needed for this part — it is there for part (b). Not every number in a question is used in every part.