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
(The answer needs to be in Watts)

Why did the car bring a calculator to the race? Because it wanted to calculate its average power! Let's get started:

For both cases, we can use the equation P = W/t, where P is the power, W is the work done, and t is the time taken.

To find the work done, we need to know the distance traveled. To calculate that, we can use the equation s = ut + (1/2)at^2, where s is the distance, u is the initial velocity (0 m/s), a is the acceleration, and t is the time.

Using this equation, we get:

s = (0) * 6.1 + (1/2) * a * (6.1)^2
s = (1/2) * a * (6.1)^2

Now, let's find the acceleration:

a = (v - u) / t
a = (21.0 - 0) / 6.1
a ≈ 3.4426 m/s^2

Now that we have the acceleration, let's calculate the distance traveled:

s = (1/2) * (3.4426) * (6.1)^2

For case A (8.0e3N), the weight of the car, we can substitute that into the equation to find the power:

P = W / t
P = (8.0e3) * [(1/2) * (3.4426) * (6.1)^2] / 6.1
P ≈ 8.0e3 * (1/2) * (3.4426) * (6.1)
P ≈ 81763.61 W (approximately)

For case B (1.2e4N), we follow the same steps:

P = W / t
P = (1.2e4) * [(1/2) * (3.4426) * (6.1)^2] / 6.1
P ≈ 1.2e4 * (1/2) * (3.4426) * (6.1)
P ≈ 122715.13 W (approximately)

So, the average power required to accelerate the car for case A is approximately 81763.61 Watts, and for case B, it is approximately 122715.13 Watts. Keep those engines running!

To find the average power required to accelerate the car, we need to calculate the work done on the car during its acceleration. We can use the equation:

Work = Force x Distance

First, let's determine the distance traveled by the car. We can use the equation for uniformly accelerating motion:

v = u + at

Where:
v = final velocity = 21.0 m/s
u = initial velocity = 0 m/s (since the car starts from rest)
a = acceleration
t = time = 6.1 s

Rearranging the equation, we get:

a = (v - u) / t

a = (21.0 m/s - 0 m/s) / 6.1 s
a = 21.0 m/s / 6.1 s
a ≈ 3.44 m/s²

Now, let's calculate the distance using the equation:

s = ut + (1/2)at²

s = 0 m/s * 6.1 s + (1/2) * 3.44 m/s² * (6.1 s)²
s = 0 + 0.5 * 3.44 m/s² * (37.21 s²)
s = 0.5 * 3.44 m/s² * 37.21 s²
s ≈ 63.96 m

Now, we can calculate the work done using the weight of the car (force) and the distance:

Work = Force x Distance

Let's start with option A) where the weight of the car is 8.0e3 N:

Work = 8.0e3 N * 63.96 m
Work = 5.1168e5 J (joules)

Finally, we can find the average power using the equation:

Average Power = Work / Time

Average Power = 5.1168e5 J / 6.1 s
Average Power ≈ 8.4e4 W (Watts)

Therefore, for option A), the average power required to accelerate the car is approximately 8.4e4 Watts.

Now, let's calculate for option B) where the weight of the car is 1.2e4 N:

Work = 1.2e4 N * 63.96 m
Work = 7.6752e5 J (joules)

Average Power = 7.6752e5 J / 6.1 s
Average Power ≈ 1.26e5 W (Watts)

Therefore, for option B), the average power required to accelerate the car is approximately 1.26e5 Watts.

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

Power = Work / Time

First, we need to calculate the work done on the car. The work done is given by the formula:

Work = force x distance

In this case, the force is equal to the weight of the car because the question states we can ignore friction. So, for each weight listed, we can calculate the work done.

A) For a weight of 8.0e3N:
Work = 8.0e3N x distance

B) For a weight of 1.2e4N:
Work = 1.2e4N x distance

To find the value of distance, we can use the formula for distance traveled during uniformly accelerated motion:

Distance = (initial velocity x time) + (1/2 x acceleration x time^2)

We are given the initial velocity (0 m/s) and the time (6.1 s) in the question. We also know that the final velocity is 21.0 m/s, and since the car starts from rest, the acceleration will be equal to the final velocity divided by the time:

Acceleration = final velocity / time

Now we can substitute the values into the formula to calculate the distance traveled for each weight.

A) For a weight of 8.0e3N:
Acceleration = 21.0 m/s / 6.1 s
Distance = (0 m/s x 6.1 s) + (1/2 x (21.0 m/s / 6.1 s) x (6.1 s)^2)

B) For a weight of 1.2e4N:
Acceleration = 21.0 m/s / 6.1 s
Distance = (0 m/s x 6.1 s) + (1/2 x (21.0 m/s / 6.1 s) x (6.1 s)^2)

Now that we have the distance traveled, we can calculate the work done for each weight.

A) For a weight of 8.0e3N:
Work = 8.0e3N x Distance

B) For a weight of 1.2e4N:
Work = 1.2e4N x Distance

Now we can substitute the calculated work values into the formula for power to find the average power required for each weight.

A) For a weight of 8.0e3N:
Power = Work / Time

B) For a weight of 1.2e4N:
Power = Work / Time

Finally, we can solve for the average power required in each case.

A) For a weight of 8.0e3N:
Power = Work / 6.1 s

B) For a weight of 1.2e4N:
Power = Work / 6.1 s

The answers will be in watts.

A) k.E = 1/2MV^2= 1/2*800*441=176400

NOW , POWER = 176400/6.1 = 2.94E2Watt
SIMILARLY SOLVE THE NEXT PART PUTTING THE GIVEN MASS