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?
Practice Questions
1 question
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?
Speed remains the same
Speed doubles
Speed increases by 41%
Speed increases by 100%
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.
Questions & Step-by-step Solutions
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Q
Q: 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?
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.
Steps: 6
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%.
