Concepts Of Physics MCQ Edition [Volume 1]PhysicsWork and Energy
A scooter company provides the following specifications for its product: Weight of the scooter — 95 kg Maximum speed — 60 km/h Maximum engine power — 3.5 hp Pick up time to reach the maximum speed — 5 s By evaluating the required power, what can be concluded about the validity of these specifications?
Options
- AThe specifications are valid, as the minimum average power required is less than the maximum engine power.
- BThe specifications are underclaimed, as the minimum average power required is less than half of the maximum en
- CThe specifications are overclaimed, as the minimum average power required to accelerate the scooter exceeds th
- DThe specifications are valid, as the maximum engine power could achieve the maximum speed in under 3 s .
Correct answer
C. The specifications are overclaimed, as the minimum average power required to accelerate the scooter exceeds th
Step-by-step solution
First, we convert the maximum speed of the scooter from km/h to m/s: v = 60 km/h = 60 5 18 m/s = 50 3 m/s The kinetic energy of the scooter at this maximum speed is: K = 1 2 mv^2 = 1 2 95 ( 50 3 )^2 = 1 2 95 2500 9 = 237500 18 13194.4 J The minimum average power required to accelerate the scooter to this speed in 5 s (ignoring air resistance and friction) is: P_ avg = K t = 13194.4 5 2638.9 W Now, we convert the maximum engine power from horsepower to Watts (using 1 hp = 746 W ): P_ max = 3.5 hp = 3.5 746 W = 2611