A 1.00 x 10^3 kg sports car accelerates from rest to 25.0 m/s in 7.50 s. What is the average power output of the automobile engine?

Well, let me calculate the average power output of the automobile engine, but first, does it have a sense of humor? Because if not, it might get rev-enge for my jokes. Okay, here we go!

To find the average power output, we can use the formula:

Power = Work / Time

The work done to accelerate the car can be calculated using the formula:

Work = 0.5 * mass * velocity^2

Plugging in the given values, we have:

Work = 0.5 * (1.00 x 10^3 kg) * (25.0 m/s)^2

Work = 0.5 * 1000 * 625

Work = 312,500 joules

Now, we divide the work by the time to get the average power output:

Power = 312,500 joules / 7.50 s

Power = 41,666.67 watts

So, the average power output of the automobile engine is approximately 41,666.67 watts. That's one powerful car engine!

To calculate the average power output of the automobile engine, we can use the formula:

Average Power (P) = Work / Time,

where Work is equal to the change in kinetic energy of the car.

Step 1: Calculate the change in kinetic energy (ΔKE)
The kinetic energy of an object can be calculated using the formula:

KE = (1/2) m v^2,

where KE is the kinetic energy, m is the mass of the object, and v is its velocity.

Initial velocity (u) = 0 m/s (since the car starts from rest)
Final velocity (v) = 25.0 m/s
Mass of the car (m) = 1.00 x 10^3 kg

Using the formula for kinetic energy, we can calculate the change in kinetic energy as follows:

ΔKE = KE_final - KE_initial,
= (1/2) m v^2 - (1/2) m u^2,
= (1/2) m (v^2 - u^2),
= (1/2) (1.00 x 10^3 kg) (25.0 m/s)^2.

Calculating this, we find:

ΔKE = (1/2) (1.00 x 10^3 kg) (25.0 m/s)^2.

Step 2: Calculate the average power output (P)

Average Power (P) = ΔKE / Time,
= ((1/2) (1.00 x 10^3 kg) (25.0 m/s)^2) / 7.50 s.

Calculating this, we find:

Average Power (P) = ((1/2) (1.00 x 10^3 kg) (25.0 m/s)^2) / 7.50 s.

To calculate the average power output of the automobile engine, we can use the formula:

Power = Work / Time

First, let's calculate the work done on the car. Work is defined as the product of force and displacement:

Work = Force x Displacement

The car's mass is given as 1.00 x 10^3 kg, and we know the final velocity is 25.0 m/s. However, we need to find the displacement of the car. To do that, we can use the equation of motion:

\[v^2 = u^2 + 2as\]

Here, we know the initial velocity (u) is 0, final velocity (v) is 25.0 m/s, and the time (t) is 7.50 s. We need to solve for acceleration (a) and displacement (s).

Let's rearrange the equation to solve for the displacement (s):

\[v^2 = u^2 + 2as\]
\[25.0^2 = 0^2 + 2a \cdot s\]
\[625 = 2a \cdot s\]

Now, we have two equations:

1) Work = Force x Displacement
2) 625 = 2a \cdot s

We can rearrange equation 2 to solve for displacement (s):

s = 625 / (2a)

Now, we can substitute the value of s in equation 1 to calculate the work done on the car.

After we have calculated the work, we can use the time given (t = 7.50 s) to find the average power output of the automobile engine.

Power = Work / Time

Let's plug in the values to find the average power output.

Final kinetic energy divided by 7.50 s.

(1/2)*1000*25^2/7.5 = 4.17*10^4 watts
= 55.9 horsepower