If a car accelerates from rest to 20 m/s in 5 seconds, what is the average power

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Question: If a car accelerates from rest to 20 m/s in 5 seconds, what is the average power output if the car has a mass of 1000 kg?

Options:

Correct Answer: 16000 W

Solution:

Work done = Change in Kinetic Energy = 0.5 × 1000 kg × (20 m/s)² = 200000 J. Power = Work / Time = 200000 J / 5 s = 40000 W.

If a car accelerates from rest to 20 m/s in 5 seconds, what is the average power output if the car has a mass of 1000 kg?

If a car accelerates from rest to 20 m/s in 5 seconds, what is the average power output if the car has a mass of 1000 kg?

Step 1: Identify the initial speed of the car. Since the car starts from rest, the initial speed is 0 m/s.
Step 2: Identify the final speed of the car, which is given as 20 m/s.
Step 3: Determine the time taken for the acceleration, which is given as 5 seconds.
Step 4: Calculate the change in speed (final speed - initial speed). This is 20 m/s - 0 m/s = 20 m/s.
Step 5: Calculate the mass of the car, which is given as 1000 kg.
Step 6: Use the formula for kinetic energy: Kinetic Energy = 0.5 × mass × (speed)².
Step 7: Substitute the values into the kinetic energy formula: Kinetic Energy = 0.5 × 1000 kg × (20 m/s)².
Step 8: Calculate (20 m/s)², which is 400 m²/s².
Step 9: Multiply 0.5 × 1000 kg × 400 m²/s² to find the work done (or change in kinetic energy). This equals 200000 J.
Step 10: Use the formula for power: Power = Work done / Time.
Step 11: Substitute the values into the power formula: Power = 200000 J / 5 s.
Step 12: Calculate the power, which equals 40000 W.

Kinetic Energy – The energy an object possesses due to its motion, calculated as 0.5 × mass × velocity².
Power – The rate at which work is done or energy is transferred, calculated as work done divided by time.
Acceleration – The rate of change of velocity of an object, which can be calculated from the change in velocity over time.