RaySix

Post

Power output of a car engine.

Created by @nathanedwards

at November 1st 2023, 3:12:37 am.

AP_Physics_1-Questions

#power

#physics

#work

Question:

A 1000 kg car is traveling at a constant speed of 20 m/s on a flat road. The car's engine provides a constant force of 3000 N to maintain this speed. Assume no other forces are acting on the car.

a) Calculate the power output of the car's engine.

b) If the car accelerates from rest to 20 m/s in 10 seconds, what is the average power output of the engine during this acceleration?

Answer:

a) To calculate the power output of the car's engine, we can use the formula:

\text{{Power}} = \text{{Force}} \times \text{{Velocity}}

Given that the force provided by the engine is 3000 N and the velocity is 20 m/s, we have:

\text{{Power}} = 3000 \, \text{N} \times 20 \, \text{m/s} = 60,000 \, \text{W}

Therefore, the power output of the car's engine is 60,000 Watts.

b) To calculate the average power output of the engine during this acceleration, we use the formula:

\text{{Power}} = \frac{{\text{{Work}}}}{{\text{{Time}}}}

In this case, the work done is equal to the change in kinetic energy of the car, given by:

\text{{Work}} = \frac{1}{2} \times \text{{Mass}} \times \text{{(Final Velocity)}^2} - \frac{1}{2} \times \text{{Mass}} \times \text{{(Initial Velocity)}^2}

Since the car is accelerating from rest, the initial velocity is 0 m/s. Therefore, the equation simplifies to:

\text{{Work}} = \frac{1}{2} \times \text{{Mass}} \times \text{{(Final Velocity)}^2}

Substituting the known values, we have:

\text{{Work}} = \frac{1}{2} \times 1000 \, \text{kg} \times (20 \, \text{m/s})^2 = 200,000 \, \text{J}

The time taken for the acceleration is given as 10 seconds, so:

\text{{Time}} = 10 \, \text{s}

Finally, we can calculate the average power output using the equation:

\text{{Power}} = \frac{{\text{{Work}}}}{{\text{{Time}}}} = \frac{{200,000 \, \text{J}}}{{10 \, \text{s}}} = 20,000 \, \text{W}

Therefore, the average power output of the engine during the acceleration is 20,000 Watts.