A 1100 kg sports car accelerates from 0m/s to 33m/s in 13s What is the average power of the engine?
To find the average power of the engine, we can use the work-energy principle. The work done on an object is equal to the change in its kinetic energy. The formula to calculate work is:
Work = Force x Distance
In this case, since we know the mass of the car and the change in velocity, we can calculate the force exerted on the car using Newton's second law of motion:
Force = Mass x Acceleration
Then, we can calculate the distance covered by the car using the formula of motion:
Distance = Initial Velocity x Time + 0.5 x Acceleration x Time^2
Finally, we can substitute the force and distance values into the work formula to get the work done on the car. The average power is then given by dividing the work by the time taken:
Average Power = Work / Time
Let's calculate the average power of the engine using these steps:
Given:
Mass of the car (m) = 1100 kg
Initial velocity (u) = 0 m/s
Final velocity (v) = 33 m/s
Time (t) = 13 s
Step 1: Calculate the force exerted on the car.
Acceleration (a) = (v - u) / t
Acceleration = (33 m/s - 0 m/s) / 13 s
Acceleration = 33 m/s / 13 s
Acceleration = 2.54 m/s^2
Force = Mass x Acceleration
Force = 1100 kg x 2.54 m/s^2
Step 2: Calculate the distance covered by the car.
Distance = Initial Velocity x Time + 0.5 x Acceleration x Time^2
Distance = 0 m/s x 13 s + 0.5 x 2.54 m/s^2 x (13 s)^2
Step 3: Calculate the work done on the car.
Work = Force x Distance
Step 4: Calculate the average power.
Average Power = Work / Time
By following these steps, you can calculate the average power of the engine for the given scenario.