If a car accelerates from rest to a speed of 20 m/s in 10 seconds, what is the a

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Question: If a car accelerates from rest to a speed of 20 m/s in 10 seconds, what is the average power output if the car has a mass of 1000 kg?

Options:

Correct Answer: 6000 W

Solution:

Work done = Change in Kinetic Energy = 0.5 × 1000 kg × (20 m/s)² = 200000 J. Power = Work / Time = 200000 J / 10 s = 20000 W.

If a car accelerates from rest to a speed of 20 m/s in 10 seconds, what is the average power output if the car has a mass of 1000 kg?

If a car accelerates from rest to a speed of 20 m/s in 10 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: Calculate the change in speed. Change in speed = final speed - initial speed = 20 m/s - 0 m/s = 20 m/s.
Step 4: Identify the mass of the car, which is given as 1000 kg.
Step 5: Calculate the change in kinetic energy using the formula: Kinetic Energy = 0.5 × mass × (speed)².
Step 6: Substitute the values into the formula: Kinetic Energy = 0.5 × 1000 kg × (20 m/s)².
Step 7: Calculate (20 m/s)², which is 400 m²/s².
Step 8: Multiply: 0.5 × 1000 kg × 400 m²/s² = 200000 J. This is the work done by the car.
Step 9: Identify the time taken for the acceleration, which is given as 10 seconds.
Step 10: Calculate the average power output using the formula: Power = Work / Time.
Step 11: Substitute the values: Power = 200000 J / 10 s.
Step 12: Calculate the power: 200000 J / 10 s = 20000 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 in this case is derived from the change in speed over time.