A car of 1,500 kg accelerates uniformly from rest to a speed of 10 m / s in 3 s.

(A) Find the work done on the car during that interval.
(B) Find the average power developed by the engine in those first 3 s.
(C) Find the instantaneous power of the motor at t = 2 s.

To find the answers to these questions, we need to use the formulas and principles of work, power, and acceleration.

(A) The work done on an object is given by the formula:

Work = Force * Distance * cos(theta),

Where Force is the net force acting on the object, Distance is the displacement of the object, and theta is the angle between the force and displacement vectors. In this case, the car starts from rest, so its initial velocity is 0 m/s. The final velocity is 10 m/s, so the change in velocity is (10 - 0) m/s = 10 m/s. The time taken is 3 s.

Using the formula for acceleration:

Acceleration = Change in Velocity / Time,

We can find the acceleration of the car:

Acceleration = 10 m/s / 3 s = 3.33 m/s^2.

As the car is accelerating uniformly, the net force acting on it is given by Newton's second law of motion:

Force = Mass * Acceleration,

Where Mass is the mass of the car. In this case, the mass of the car is 1,500 kg. Substituting the values:

Force = 1,500 kg * 3.33 m/s^2 = 4,995 N.

Now we can calculate the work done on the car:

Work = Force * Distance * cos(theta),

where theta is the angle between the force and displacement vectors. As the car is accelerating in the same direction as the force, theta is 0 degrees, and cos(0) = 1. So, the work done is:

Work = 4,995 N * Distance * 1 = 4,995 N * Distance.

We need the value of Distance to calculate the work done.

(B) Average power is given by the formula:

Average Power = Work / Time,

where Work is the work done on the car and Time is the time taken. We've already calculated the work done in part A and the time taken is 3 s. So, we can calculate the average power as:

Average Power = Work / Time = 4,995 N * Distance / 3 s.

(C) The instantaneous power is given by the formula:

Instantaneous Power = Force * Velocity,

where Force is the net force acting on the car and Velocity is the instantaneous velocity at a given time. At t = 2 s, we can calculate the instantaneous power as:

Instantaneous Power = Force * Velocity = 4,995 N * Velocity.

We need the value of Velocity at t = 2 s to calculate the instantaneous power. By using the formula for uniform acceleration:

Velocity = Initial Velocity + Acceleration * Time,

initial velocity is 0 m/s, acceleration is 3.33 m/s^2, and time is 2 s. Substituting the values:

Velocity = 0 m/s + 3.33 m/s^2 * 2 s = 6.66 m/s.

Now we can calculate the instantaneous power at t = 2 s:

Instantaneous Power = 4,995 N * 6.66 m/s.

Using these formulas and calculations, you can find the answers to the questions (A), (B), and (C) related to the car's acceleration, work done, and power.