A car of mas 1500kg has a maximum speed of 1500kg/h on a level road when working at a maximum power against resistance force of 60N.Find the maximum power of the engine?

To find the maximum power of the engine, we first need to calculate the maximum force that the engine can overcome at the maximum speed.

Given:
Mass of the car (m) = 1500 kg
Maximum speed (v) = 1500 km/h = 416.67 m/s
Resistance force (F) = 60 N

The maximum power (P) can be calculated using the formula:

P = F * v

Substitute the values:

P = 60 N * 416.67 m/s
P = 25000 W

Therefore, the maximum power of the engine is 25000 Watts or 25 kW.

The work done by the engine against the resistance force is equal to the change in kinetic energy of the car.

$$W = F\times d = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$$

$$W = F\times d = \frac{1}{2}m(v^2 - u^2)$$

$$W = 60N \times (1500km/h)^2 = 1.35\times 10^6J$$

The power is equal to the work done divided by the time taken.

$$P = \frac{W}{t}$$

The time taken to reach the maximum speed can be calculated using the formula:

$$v = u + at$$

$$t = \frac{v - u}{a}$$

The acceleration of the car is equal to the force divided by the mass.

$$a = \frac{F}{m}$$

$$a = \frac{60N}{1500kg} = 0.04m/s^2$$

$$t = \frac{1500km/h - 0}{0.04m/s^2} = 104.17s$$

Therefore, the maximum power of the engine is:

$$P = \frac{1.35\times 10^6J}{104.17s} = \boxed{13kW}$$