A 1300 kg sports car accelerates from rest to 85 km/h in 6.2 s. What is the average power delivered by the engine?
Work done = Kinetic energy
Work done = 1/2(mv^2)
= 1/2(1300kg)(7225km/h)
= 1/2(93925000)
= 46962500J
Power = Work Done/Time
Power = 46962500/6.2
= 7,574,596.774 W
To find the average power delivered by the engine, we can use the equation:
average power = work / time
The work done is given by the equation:
work = force x distance
The force can be calculated using Newton's second law:
force = mass x acceleration
First, we need to convert the speed of the car from km/h to m/s. We know that 1 km/h is equal to 0.2778 m/s. So,
85 km/h = 85 x 0.2778 = 23.6111 m/s
The acceleration can be calculated using the formula:
acceleration = (final velocity - initial velocity) / time
Plugging in the given values:
acceleration = (23.6111 m/s - 0 m/s) / 6.2 s = 3.80614 m/s²
Now we can calculate the force:
force = mass x acceleration = 1300 kg x 3.80614 m/s² = 4948.999 N
The distance traveled can be calculated using the equation:
distance = (initial velocity x time) + (0.5 x acceleration x time²)
Plugging in the values:
distance = (0 m/s x 6.2 s) + (0.5 x 3.80614 m/s² x (6.2 s)²) = 72.735 m
Now we can calculate the work done:
work = force x distance = 4948.999 N x 72.735 m = 360038.543 J
Finally, we can calculate the average power:
average power = work / time = 360038.543 J / 6.2 s = 58099.757 W
Therefore, the average power delivered by the engine is approximately 58099.757 Watts.
To find the average power delivered by the engine, we can use the equation:
Power = (Work done) / (Time taken)
First, let's find the work done by the car. We know that work is equal to the change in kinetic energy. The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity^2
The car starts from rest, so its initial velocity is 0. The final velocity is 85 km/h, which needs to be converted to m/s:
85 km/h = (85 * 1000) / (60 * 60) m/s
≈ 23.6 m/s
Now we can calculate the change in kinetic energy:
Change in Kinetic Energy = (1/2) * mass * (final velocity^2 - initial velocity^2)
= (1/2) * 1300 kg * (23.6 m/s)^2 - 0^2
= (1/2) * 1300 kg * (23.6 m/s)^2
≈ 1703200 J
Next, we need to calculate the time in seconds. The given time is 6.2 s.
Now we can calculate the average power:
Power = (Work done) / (Time taken)
= 1703200 J / 6.2 s
≈ 274968 W
Therefore, the average power delivered by the engine is approximately 274968 Watts.