A car accelerates uniformly from rest to 21.0 m/s in 6.1 s along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if the weight of the car is the following.

A) 8.0e3N B) 1.2e4N

To determine the average power required to accelerate the car, we need to use the formula:

Power = Work / Time

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

Work = Force * Distance

Since the car is initially at rest, the work done will be equal to its change in kinetic energy:

Work = ΔKE = KE_final - KE_initial

Since the car starts from rest, the initial kinetic energy (KE_initial) is zero, so the work done is:

Work = KE_final

To find the final kinetic energy (KE_final), we can use the formula:

KE_final = 0.5 * mass * velocity^2

where mass is the weight of the car divided by the acceleration due to gravity (g = 9.8 m/s^2).

Let's calculate the average power for each case:

A) Weight of the car = 8.0e3 N

mass = weight / g = 8.0e3 N / 9.8 m/s^2 = 816.33 kg

KE_final = 0.5 * 816.33 kg * (21.0 m/s)^2 = 177847.79 J

Work = KE_final = 177847.79 J

Average power = Work / Time = 177847.79 J / 6.1 s = 29144.92 W

B) Weight of the car = 1.2e4 N

mass = weight / g = 1.2e4 N / 9.8 m/s^2 = 1224.49 kg

KE_final = 0.5 * 1224.49 kg * (21.0 m/s)^2 = 506471.67 J

Work = KE_final = 506471.67 J

Average power = Work / Time = 506471.67 J / 6.1 s = 82979.27 W

Therefore,

A) The average power required to accelerate the car with a weight of 8.0e3 N is 29144.92 W.
B) The average power required to accelerate the car with a weight of 1.2e4 N is 82979.27 W.

To determine the average power required to accelerate the car, we can use the formula:

Power = (Force x displacement) / time

From the given information, we first need to calculate the force required to accelerate the car. We can do this using Newton's second law of motion:

Force = mass x acceleration

Since the mass of the car is not given, we can use the weight of the car as a substitute. The weight of an object can be calculated using the formula:

Weight = mass x acceleration due to gravity

The acceleration due to gravity is approximately 9.8 m/s². Therefore, we can find the mass of the car by dividing its weight by the acceleration due to gravity.

Once we have the force, we can use it to calculate the power. Let's calculate the average power required for each weight:

A) Weight = 8.0e3 N

Mass = Weight / Acceleration due to gravity
Mass = 8.0e3 N / 9.8 m/s²

Next, we need to find the acceleration of the car using the formulas:

Acceleration = (final velocity - initial velocity) / time

Acceleration = (21.0 m/s - 0) / 6.1 s

Now we can calculate the force:

Force = Mass x Acceleration

Finally, we can calculate the power:

Power = (Force x Displacement) / Time

B) Weight = 1.2e4 N

Repeat the above steps by substituting the weight value of 1.2e4 N.

These calculations will give us the respective average power required to accelerate the car for each given weight.