A cyclist is moving at a speed of 10 m/s. If he doubles his speed, how much more kinetic energy will he have? (2023)

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Q: A cyclist is moving at a speed of 10 m/s. If he doubles his speed, how much more kinetic energy will he have? (2023)

Solution: Kinetic Energy is proportional to the square of the speed. If speed is doubled, KE increases by a factor of 2^2 = 4.

Steps: 7

Step 1: Understand that Kinetic Energy (KE) is calculated using the formula KE = 0.5 * mass * speed^2.
Step 2: Identify the initial speed of the cyclist, which is 10 m/s.
Step 3: Calculate the initial Kinetic Energy using the formula: KE_initial = 0.5 * mass * (10 m/s)^2.
Step 4: Determine the new speed after doubling, which is 20 m/s (10 m/s * 2).
Step 5: Calculate the new Kinetic Energy using the formula: KE_new = 0.5 * mass * (20 m/s)^2.
Step 6: Compare the new Kinetic Energy to the initial Kinetic Energy to find the increase: KE_increase = KE_new - KE_initial.
Step 7: Since KE is proportional to the square of the speed, doubling the speed increases KE by a factor of 4.