A cyclist accelerates from rest to a speed of 10 m/s in 5 seconds. What is the average power output if the cyclist has a mass of 70 kg?

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Q: A cyclist accelerates from rest to a speed of 10 m/s in 5 seconds. What is the average power output if the cyclist has a mass of 70 kg?

Solution: Kinetic Energy = 0.5 × m × v² = 0.5 × 70 kg × (10 m/s)² = 3500 J. Power = Work / Time = 3500 J / 5 s = 700 W.

Steps: 10

Step 1: Identify the mass of the cyclist, which is 70 kg.
Step 2: Identify the final speed of the cyclist, which is 10 m/s.
Step 3: Identify the time taken to reach this speed, which is 5 seconds.
Step 4: Calculate the Kinetic Energy using the formula: Kinetic Energy = 0.5 × mass × speed².
Step 5: Substitute the values into the formula: Kinetic Energy = 0.5 × 70 kg × (10 m/s)².
Step 6: Calculate (10 m/s)², which is 100 m²/s².
Step 7: Multiply 0.5 × 70 kg × 100 m²/s² to get Kinetic Energy = 3500 J.
Step 8: Use the formula for Power, which is Power = Work / Time.
Step 9: Substitute the values: Power = 3500 J / 5 s.
Step 10: Calculate the Power to find that it equals 700 W.