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A cyclist accelerates from rest to a speed of 15 m/s. If the mass of the cyclist

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Question: A cyclist accelerates from rest to a speed of 15 m/s. If the mass of the cyclist and the bicycle is 75 kg, what is the work done by the cyclist?

Options:

  1. 800 J
  2. 900 J
  3. 1000 J
  4. 1200 J

Correct Answer: 1000 J

Solution: 

Work done = Change in Kinetic Energy = 0.5 × mass × (final velocity² - initial velocity²) = 0.5 × 75 kg × (15 m/s)² = 843.75 J.

A cyclist accelerates from rest to a speed of 15 m/s. If the mass of the cyclist

Practice Questions

Q1
A cyclist accelerates from rest to a speed of 15 m/s. If the mass of the cyclist and the bicycle is 75 kg, what is the work done by the cyclist?
  1. 800 J
  2. 900 J
  3. 1000 J
  4. 1200 J

Questions & Step-by-Step Solutions

A cyclist accelerates from rest to a speed of 15 m/s. If the mass of the cyclist and the bicycle is 75 kg, what is the work done by the cyclist?
  • Step 1: Identify the initial speed of the cyclist. Since the cyclist starts from rest, the initial speed is 0 m/s.
  • Step 2: Identify the final speed of the cyclist. The final speed is given as 15 m/s.
  • Step 3: Identify the mass of the cyclist and the bicycle. The mass is given as 75 kg.
  • Step 4: Use the formula for kinetic energy, which is KE = 0.5 × mass × (velocity)².
  • Step 5: Calculate the change in kinetic energy. Since the initial kinetic energy is 0 (because the initial speed is 0), we only need to calculate the final kinetic energy.
  • Step 6: Plug in the values into the formula: KE = 0.5 × 75 kg × (15 m/s)².
  • Step 7: Calculate (15 m/s)², which is 225 m²/s².
  • Step 8: Multiply 0.5 × 75 kg × 225 m²/s² to get the final result.
  • Step 9: The result is 8437.5 J, which is the work done by the cyclist.
  • Work-Energy Principle – The work done on an object is equal to the change in its kinetic energy.
  • Kinetic Energy Formula – Kinetic energy is calculated using the formula KE = 0.5 × mass × velocity².
  • Units of Work – Work is measured in joules (J), which is equivalent to kg·m²/s².
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