A 2300. kg car starts from rest and accelerates uniformly to 24.0 m/s in 24.0 s. Assume that air resistance remains constant at 510 N during this time. Find (a) the net force on the car

b) the average power developed by the engine?
c) the instantaneous power output of the engine at t = 24.0 s, just before the car stops accelerating.

To find the answers to these questions, we need to use the equations of motion and the concept of power.

(a) The net force on the car can be found using Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. In this case, the acceleration is the change in velocity divided by the time taken. So, the net force can be calculated as follows:

Net force = mass × acceleration

Acceleration = (final velocity - initial velocity) / time
Acceleration = (24.0 m/s - 0 m/s) / 24.0 s
Acceleration = 1.0 m/s^2

Net force = 2300 kg × 1.0 m/s^2
Net force = 2300 N

Therefore, the net force on the car is 2300 N.

(b) The average power developed by the engine can be calculated using the equation:

Average power = work done / time

Work done can be found using the formula:

Work done = force × distance

In this case, the force acting on the car is the net force (2300 N) minus the constant air resistance (510 N) and the distance traveled by the car can be found by using the equation of motion:

Distance = initial velocity × time + 0.5 × acceleration × time^2

Distance = 0 m/s × 24.0 s + 0.5 × 1.0 m/s^2 × (24.0 s)^2
Distance = 288.0 m

Work done = (2300 N - 510 N) × 288.0 m
Work done = 488160 J

Average power = 488160 J / 24.0 s
Average power = 20340 W

Therefore, the average power developed by the engine is 20340 W.

(c) The instantaneous power output of the engine can be calculated at the point when the car stops accelerating. At this point, the net force on the car will be equal to the air resistance.

Net force = air resistance

So, the instantaneous power output can be calculated using the formula:

Instantaneous power = force × velocity

Force = air resistance = 510 N
Velocity = final velocity of the car = 24.0 m/s

Instantaneous power = 510 N × 24.0 m/s
Instantaneous power = 12240 W

Therefore, the instantaneous power output of the engine at t = 24.0 s is 12240 W.