Question:

A car of mass 1000 kg is accelerating with a constant force of 500 N along a horizontal road. The car covers a distance of 500 m in 20 seconds. Calculate the power exerted by the car's engine.

Assume there is no friction or air resistance.

Answer:

Given: Mass of the car, m = 1000 kg Force applied on the car, F = 500 N Distance covered by the car, d = 500 m Time taken, t = 20 s

Power (P) is defined as the rate at which work is done or energy is transferred. It can be calculated as the product of force and velocity.

Power = Force × Velocity

To find the velocity, we first need to calculate the acceleration using the equation:

Acceleration (a) = Force / Mass

Substituting the given values, we find:

a = 500 N / 1000 kg a = 0.5 m/s^2

Next, we need to find the velocity of the car using the equation:

Velocity (v) = initial velocity + acceleration × time

Since the car starts from rest, the initial velocity is zero.

v = 0 + 0.5 m/s^2 × 20 s v = 10 m/s

Finally, we can calculate the power:

P = Force × Velocity P = 500 N × 10 m/s P = 5000 J/s (or Watts)

Therefore, the power exerted by the car's engine is 5000 Watts.