A car accelerates uniformly from rest to 18.4 m/s in 4.36 s along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if (a) the weight of the car is 6.11 x 103 N, and (b) the weight of the car is 1.01 x 104 N.

Well, well, well! Looks like you need some help with physics, huh? Don't worry, I'm here to clown around and assist you! Let's get down to business and solve these problems.

(a) To find the average power required to accelerate the car, we can use the formula for power: P = W/t, where P is the power, W is the work done, and t is the time interval.

First, we need to find the work done. Since the car is accelerating uniformly, we can use the equation W = Fd, where W is the work done, F is the force applied, and d is the displacement. In this case, we can calculate the force using Newton's second law, F = ma, where F is the force, m is the mass of the car, and a is the acceleration.

Now, we know the weight of the car is the force due to gravity, W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity. Rearranging this equation, we have m = W/g.

So, let's plug in the values! We have m = 6.11 x 10^3 N / 9.8 m/s^2, since g is approximately 9.8 m/s^2. Solving for m, we get the mass of the car.

Now, we need to find the acceleration. We know that the car starts from rest, so the initial velocity, u, is 0 m/s. The final velocity, v, is given as 18.4 m/s. The time interval, t, is 4.36 s. We can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time interval. Rearranging this equation, we have a = (v - u)/t.

Plug in the numbers again! We have a = (18.4 m/s - 0 m/s) / 4.36 s. Solve this equation to find the acceleration.

Great, now we have the mass and the acceleration! We can finally calculate the work done using W = Fd. Remember, F = ma, where m is the mass we calculated, and a is the acceleration we found. We also know that d = vt, where v is the final velocity and t is the time interval. Plug in the values and solve the equation.

Now that we have the work done, we can calculate the average power! Just divide the work done by the time interval, P = W/t.

Phew! That was quite a journey, wasn't it? Now go ahead and calculate the average power required to accelerate the car with these values. Don't forget to let me know the answer, so I can clown around some more with you!

(b) Oh, another problem? You're officially driving me nuts! But don't worry, I'm still here to help you.

For part (b), we need to apply the same process as we did for part (a). We'll use the given weight of the car, which is 1.01 x 10^4 N, and follow the steps to find the average power.

Remember, the process includes finding the mass, acceleration, work done, and finally, the average power.

After you've completed all the calculations, let me know your answer! I'll be waiting here, juggling some clown noses in the meantime.

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

Power = Work / Time

First, we need to calculate the work done on the car to accelerate it. The work done is equal to the change in kinetic energy, which can be calculated using:

Work = (1/2) * Mass * (Final Velocity^2 - Initial Velocity^2)

To find the mass of the car, we can use the weight and the acceleration due to gravity, using the formula:

Weight = Mass * Gravity

Rearranging the formula, we get:

Mass = Weight / Gravity

Now, let's calculate the average power for each case:

(a) Weight of the car is 6.11 x 10^3 N:

First, calculate the mass of the car:

Mass = 6.11 x 10^3 N / 9.8 m/s^2 ≈ 624.5 kg

Next, calculate the work done:

Initial Velocity = 0 m/s
Final Velocity = 18.4 m/s

Work = (1/2) * 624.5 kg * (18.4 m/s)^2 - (0 m/s)^2
≈ 133,216 J

Finally, calculate the average power:

Time = 4.36 s

Power = Work / Time
= 133,216 J / 4.36 s
≈ 30,576 W

Therefore, the average power required to accelerate the car when the weight is 6.11 x 10^3 N is approximately 30,576 W.

(b) Weight of the car is 1.01 x 10^4 N:

Repeat the same steps as above, but with a different weight:

Mass = 1.01 x 10^4 N / 9.8 m/s^2 ≈ 1,030.6 kg

Work = (1/2) * 1,030.6 kg * (18.4 m/s)^2 - (0 m/s)^2
≈ 340,512 J

Power = Work / Time
= 340,512 J / 4.36 s
≈ 78,182 W

Therefore, the average power required to accelerate the car when the weight is 1.01 x 10^4 N is approximately 78,182 W.