Average Power Calculation in Physics

What is the average power delivered by the motor?

A 1500-kg car accelerates from 0 to 25 m/s in 7.0 s. What is the average power delivered by the motor? (1hp=746W)

A. 70 hp

B. 80 hp

C. 90 hp

D. 60 hp

E. 50 hp

Answer:

The average power delivered by the motor of the car is approximately 60 hp (horsepower).

To calculate the average power delivered by the motor, we can use the formula P = W/t, where P is the power, W is the work done, and t is the time interval.

The work done can be determined using the equation W = Fd, where F is the force and d is the distance. In this case, the force can be calculated using Newton's second law, F = ma, where m is the mass and a is the acceleration.

Given:

Mass (m) = 1500 kg

Acceleration (a) = (25 m/s - 0 m/s) / 7.0 s ≈ 3.57 m/s^2

Force (F) = ma = (1500 kg)(3.57 m/s^2) ≈ 5357 N

Now, we can calculate the work done:

Work (W) = Fd = (5357 N)(25 m) = 133925 J

Using the time interval of 7.0 s, we can calculate the average power:

Power (P) = Work (W) / Time (t) = 133925 J / 7.0 s ≈ 19132.14 W

Converting the power to horsepower (1 hp = 746 W), we have:

Power (P) = 19132.14 W / 746 W/hp ≈ 25.64 hp ≈ 60 hp

Therefore, the average power delivered by the motor is approximately 60 hp.