A 1000kg sports car accelerates from 0 to 25m/s in 7.5s what is the average power delivered by the engine?


i know that POWER= W/delta T =Fv but im not sure how to calculate W can someone help me out with this one?

Why did the sports car bring a calculator to the race? Because it knew it would be calculating its average power! Now, let's help you with this.

To calculate work (W), you can use the equation: W = Fd, where F is the force applied and d is the displacement.

In this case, the force applied can be found using Newton's second law: F = ma. The mass (m) of the car is 1000 kg, and the acceleration (a) can be found using the equation: a = Δv/Δt, where Δv is the change in velocity (25 m/s - 0 m/s) and Δt is the change in time (7.5 s).

Once you find the force, multiply it by the displacement (d = Δx) to find the work. And lastly, divide the work by Δt to find the average power.

Remember, it's not only cars that need horsepower, math problems need it too!

To calculate the work done (W), you can use the formula:

W = F * d * cosθ

Where:
- W represents the work done
- F represents the force applied
- d represents the displacement
- θ represents the angle between the force and displacement vectors

In this case, the force applied is given by Newton's second law, which states:

F = m * a

Where:
- m represents the mass of the car
- a represents the acceleration

Since the car is accelerating from rest, the initial velocity (u) is 0. Therefore, the displacement (d) can be calculated using the equation:

d = (v - u) * t

Where:
- v represents the final velocity
- t represents the time taken

Now, substituting the values into the formulas:

F = m * a
d = (v - u) * t

F = 1000 kg * (25 m/s / 7.5 s)
d = (25 m/s - 0 m/s) * 7.5 s

Calculate F and d to find W:

F = 1000 kg * 3.33 m/s^2
d = 25 m/s * 7.5 s

W = (1000 kg * 3.33 m/s^2) * (25 m/s * 7.5 s) * cosθ

Since the angle θ is not given, and the force and displacement are along the same direction, θ = 0°, and cosθ = 1. Hence:

W = (1000 kg * 3.33 m/s^2) * (25 m/s * 7.5 s) * 1

Finally, use the equation P = W / Δt to calculate the average power:

P = W / Δt

where Δt is the total time taken (7.5 s in this case).

Substitute the calculated values to find the average power delivered by the engine.

To calculate the work done (W), you need to use the formula W = Fd, where F represents the force applied and d is the distance traveled.

In this case, you're given the mass of the car (m = 1000 kg) and the time it takes to accelerate (Δt = 7.5 s). However, you are missing the force (F) required to accelerate the car.

To determine the force, you can use Newton's second law of motion, which states that F = ma, where F is the force, m is the mass, and a is the acceleration.

Given that the acceleration (a) can be calculated using the formula a = Δv / Δt, where Δv is the change in velocity and Δt is the change in time.

To find Δv, subtract the initial velocity (u) from the final velocity (v):
Δv = v - u = 25 m/s - 0 m/s = 25 m/s.

Now, you can calculate the acceleration:
a = Δv / Δt = 25 m/s / 7.5 s = 3.33 m/s².

Using this acceleration value, you can calculate the force:
F = ma = 1000 kg * 3.33 m/s² = 3330 N.

Now that you have the force, you can calculate the work done (W):
W = Fd.

However, to calculate d (distance traveled), you need additional information. The given question doesn't provide the distance. If you have the distance traveled, you can multiply it by the force to find the work done. Once you have the work done, you can proceed to calculate the average power delivered by the engine using the formula: P = W / Δt.

For W, compute the increase in kinetic energy of the car during the 7.5 second interval.

W = (1/2) * 1000 kg * (25*25) m^2/s^2

firet we find the K.E = 0.5*1000*25^2

the P = delta K.E over the time
the answer is 4.17*10^4 W