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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Work and Energy

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Work and Energy

A scooter company provides the following specifications for its...

A scooter company provides the following specifications for its product:
Weight of the scooter — 95 kg95 \text{ kg}
Maximum speed — 60 km/h60 \text{ km/h}
Maximum engine power — 3.5 hp3.5 \text{ hp}
Pick up time to reach the maximum speed — 5 s5 \text{ s}
By evaluating the required power, what can be concluded about the validity of these specifications?

Options

  1. AThe specifications are valid, as the minimum average power required is less than the maximum engine power.
  2. BThe specifications are underclaimed, as the minimum average power required is less than half of the maximum engine power.
  3. CThe specifications are overclaimed, as the minimum average power required to accelerate the scooter exceeds the maximum engine power.
  4. DThe specifications are valid, as the maximum engine power could achieve the maximum speed in under 3 s3 \text{ s}.

Correct answer

C. The specifications are overclaimed, as the minimum average power required to accelerate the scooter exceeds the maximum engine power.

Step-by-step solution

First, we convert the maximum speed of the scooter from km/h to m/s:

v=60 km/h=60×518 m/s=503 m/sv = 60 \text{ km/h} = 60 \times \dfrac{5}{18} \text{ m/s} = \dfrac{50}{3} \text{ m/s}

The kinetic energy of the scooter at this maximum speed is:

K=12mv2=12×95×(503)2=12×95×25009=23750018≈13194.4 JK = \dfrac{1}{2}mv^2 = \dfrac{1}{2} \times 95 \times \left(\dfrac{50}{3}\right)^2 = \dfrac{1}{2} \times 95 \times \dfrac{2500}{9} = \dfrac{237500}{18} \approx 13194.4 \text{ J}

The minimum average power required to accelerate the scooter to this speed in 5 s5 \text{ s} (ignoring air resistance and friction) is:

Pavg=Kt=13194.45≈2638.9 WP_{avg} = \dfrac{K}{t} = \dfrac{13194.4}{5} \approx 2638.9 \text{ W}

Now, we convert the maximum engine power from horsepower to Watts (using 1 hp=746 W1 \text{ hp} = 746 \text{ W}):

P_\max = 3.5 \text{ hp} = 3.5 \times 746 \text{ W} = 2611 \text{ W}

Comparing the required average power and the maximum engine power:

P_{avg} \approx 2638.9 \text{ W} > P_\max = 2611 \text{ W}

Since the minimum average power required to achieve the given specifications exceeds the maximum power the engine can produce, the specifications are overclaimed.
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