A 1300 kg sports car accelerates from rest to 90 km/h in 7.0 s. What is the average power delivered by the engine?

power= Kineticnergychange/time= 1/2 mv^2 /7

where v is in m/s

58035kw

To find the average power delivered by the engine, we can use the formula:

Power = (Work done) / (Time taken)

First, let's find the work done by the car. The work done is equal to the change in kinetic energy of the car. The formula to calculate kinetic energy is:

Kinetic Energy = (1/2) * Mass * (Velocity)^2

Initial velocity of the car, u = 0 m/s (since the car starts from rest)
Final velocity of the car, v = 90 km/h = (90 * 1000) / 3600 = 25 m/s (converting km/h to m/s)

Using the formula, the change in kinetic energy is:
Change in kinetic energy = (1/2) * Mass * (Final velocity)^2 - (1/2) * Mass * (Initial velocity)^2

= (1/2) * 1300 kg * (25 m/s)^2 - (1/2) * 1300 kg * (0 m/s)^2

= (1/2) * 1300 kg * (625 m^2/s^2) - 0

= 406,250 J

Now, let's calculate the average power:

Average power = Work done / Time taken

Time taken = 7.0 s

Average power = 406,250 J / 7.0 s

= 58,036 W

Therefore, the average power delivered by the engine is 58,036 watts.

To find the average power delivered by the engine, we can use the formula:

Power = (Force × Distance) ÷ Time

First, we need to calculate the force applied by the engine. We can use Newton's second law of motion, which states:

Force = Mass × Acceleration

Given:
Mass (m) = 1300 kg
Acceleration (a) = Change in velocity ÷ Time = (90 km/h - 0 km/h) ÷ (7.0 s)

First, let's convert the velocity from km/h to m/s:
1 km/h = 1000 m/3600 s = 5/18 m/s

So, the change in velocity is:
(90 km/h - 0 km/h) = 90 km/h
= 90 × (5/18 m/s)
= 25 m/s

Now, we can calculate the acceleration:
Acceleration (a) = (25 m/s) ÷ (7.0 s)

Next, we can calculate the force:
Force = Mass × Acceleration
Force = 1300 kg × (25 m/s) ÷ (7.0 s)

Now, we have calculated the force applied by the engine. The next step is to calculate the distance traveled by the car during this time.

We can use the formula:

Distance = 0.5 × Acceleration × Time^2

Distance = 0.5 × (25 m/s) × (7.0 s)^2

Finally, we can substitute the force and distance values back into the power formula:

Power = (Force × Distance) ÷ Time

This will give us the average power delivered by the engine.