A motorist driving a 1200-kg car on level ground accelerates from 20.0 m/s to 30.0 m/s in a time of 5.0s. Neglecting friction and air resistance, determine the average mechanical power in watts the engine must supply during this time interval.

a = (Vf - Vo) / t,

a = (30 - 20)m/s / 5s = 2m/s^2.

Fc = mg = 1200kg * 9.8N/kg = 11760N.

(Vf)^2 = Vo^2 + 2ad = (30)^2,
(20)^2 + 2 * 2 * d = 900,
400 + 4d = 900,
4d = 900 - 400 = 500,
d = 125m. = Distance traveled during
acceleration.

P = F*d / t = 11760 * 125 / 5 = 294000W

To determine the average mechanical power the engine must supply during the time interval, we can use the formula for power:

Power = Force x Velocity

In this case, we need to find the force exerted by the engine to accelerate the car. We can use Newton's second law of motion:

Force = Mass x Acceleration

Given:
Mass (m) = 1200 kg
Initial velocity (v₁) = 20.0 m/s
Final velocity (v₂) = 30.0 m/s
Time (t) = 5.0 s

First, let's find the acceleration:
Acceleration (a) = (Change in velocity) / (Time)
a = (v₂ - v₁) / t
a = (30.0 m/s - 20.0 m/s) / 5.0 s
a = 10.0 m/s²

Now, we can find the force:
Force = Mass x Acceleration
Force = 1200 kg x 10.0 m/s²
Force = 12,000 N

Finally, we can calculate the average mechanical power:
Power = Force x Velocity
Power = 12,000 N x 25.0 m/s (average velocity between v₁ and v₂)
Power = 300,000 W (or 300 kW)

Therefore, the average mechanical power the engine must supply during this time interval is 300,000 watts (or 300 kilowatts).

To determine the average mechanical power, we need to calculate the work done and divide it by the time interval.

First, let's calculate the work done using the formula for work:

Work (W) = Force (F) × Distance (d)

In this case, the force is the net force acting on the car, which is given by Newton's second law:

F = mass (m) × acceleration (a)

The distance the car travels during this time interval is given by:

d = (initial velocity + final velocity) / 2 × time

Now we can substitute the given values into the equations:

m = 1200 kg (mass of car)
a = (final velocity - initial velocity) / time = (30.0 m/s - 20.0 m/s) / 5.0 s = 2.0 m/s^2 (acceleration)
d = (20.0 m/s + 30.0 m/s) / 2 × 5.0 s = 25.0 m (distance)

Now we can calculate the force and then the work:

F = m × a = 1200 kg × 2.0 m/s^2 = 2400 N (force)
W = F × d = 2400 N × 25.0 m = 60000 J (work)

Finally, we can calculate the average mechanical power:

Power (P) = Work (W) / Time (t) = 60000 J / 5.0 s

P ≈ 12000 watts

Therefore, the engine must supply an average mechanical power of approximately 12000 watts during this time interval.