A cyclist is moving with a speed of 10 m/s. If he doubles his speed, how much mo

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

Options:

Correct Answer: 4 times

Exam Year: 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.

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

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

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 in kinetic energy.
Step 7: Since KE is proportional to the square of the speed, doubling the speed increases KE by a factor of 4.

Kinetic Energy – Kinetic Energy (KE) is calculated using the formula KE = 0.5 * m * v^2, where m is mass and v is velocity. It demonstrates that KE is proportional to the square of the speed.
Proportional Relationships – Understanding how changes in speed affect kinetic energy through proportional relationships, specifically that doubling the speed results in a fourfold increase in kinetic energy.