A 1000 kg car accelerates from rest to a speed of 20 m/s in 10 seconds. What is

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Question: A 1000 kg car accelerates from rest to a speed of 20 m/s in 10 seconds. What is the average power exerted by the engine?

Options:

Correct Answer: 5000 W

Solution:

First, calculate the work done: W = (1/2)mv^2 = (1/2)(1000 kg)(20 m/s)^2 = 200000 J. Then, power is P = W/t = 200000 J / 10 s = 20000 W.

A 1000 kg car accelerates from rest to a speed of 20 m/s in 10 seconds. What is the average power exerted by the engine?

A 1000 kg car accelerates from rest to a speed of 20 m/s in 10 seconds. What is the average power exerted by the engine?

Correct Answer: 20000 W

Step 1: Identify the mass of the car, which is 1000 kg.
Step 2: Identify the final speed of the car, which is 20 m/s.
Step 3: Identify the time taken to reach that speed, which is 10 seconds.
Step 4: Use the formula for work done (W) when accelerating an object: W = (1/2)mv^2.
Step 5: Plug in the values: W = (1/2)(1000 kg)(20 m/s)^2.
Step 6: Calculate (20 m/s)^2, which is 400 m^2/s^2.
Step 7: Multiply: W = (1/2)(1000 kg)(400 m^2/s^2) = 200000 J.
Step 8: Use the formula for power (P): P = W/t.
Step 9: Plug in the values: P = 200000 J / 10 s.
Step 10: Calculate the power: P = 20000 W.

Kinetic Energy – The work done on the car is equal to the change in its kinetic energy, calculated using the formula W = (1/2)mv^2.
Power – Power is defined as the rate at which work is done, calculated using the formula P = W/t.
Units of Measurement – Understanding the units of work (Joules) and power (Watts) is essential for solving the problem.