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A cyclist is pedaling at a constant speed and exerts a power of 200 W. If the cy

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Question: A cyclist is pedaling at a constant speed and exerts a power of 200 W. If the cyclist increases their power output to 400 W, what happens to their speed assuming no other forces act?

Options:

  1. Speed remains the same
  2. Speed doubles
  3. Speed increases by 41%
  4. Speed increases by 100%

Correct Answer: Speed increases by 41%

Solution: 

Power is proportional to the cube of the speed in cycling. If power doubles, speed increases by a factor of (2)^(1/3) which is approximately 1.26, or about a 41% increase.

A cyclist is pedaling at a constant speed and exerts a power of 200 W. If the cy

Practice Questions

Q1
A cyclist is pedaling at a constant speed and exerts a power of 200 W. If the cyclist increases their power output to 400 W, what happens to their speed assuming no other forces act?
  1. Speed remains the same
  2. Speed doubles
  3. Speed increases by 41%
  4. Speed increases by 100%

Questions & Step-by-Step Solutions

A cyclist is pedaling at a constant speed and exerts a power of 200 W. If the cyclist increases their power output to 400 W, what happens to their speed assuming no other forces act?
  • Step 1: Understand that power in cycling is related to speed. When a cyclist pedals, the power they exert affects how fast they can go.
  • Step 2: Know that power is proportional to the cube of the speed. This means if you change the power, the speed changes in a specific way.
  • Step 3: In this case, the cyclist's power increases from 200 W to 400 W. This is a doubling of power.
  • Step 4: To find out how speed changes, we use the formula that relates power and speed: if power doubles, speed increases by a factor of (2)^(1/3).
  • Step 5: Calculate (2)^(1/3). This is approximately 1.26.
  • Step 6: This means the new speed is about 1.26 times the original speed, which is an increase of about 26%.
  • Power and Speed Relationship – The relationship between power output and speed in cycling, where power is proportional to the cube of speed.
  • Proportionality and Exponents – Understanding how changes in one variable (power) affect another variable (speed) through exponentiation.
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