A 1200 kg sports car accelerates from 0 to 60.0 mph (27.0 m/s) in 5.20 seconds.
What is the average power developed in watts?
In kilowatts?
gain in Kinetic energy = work done
= (1/2) 1200 27^2 Joules
divide by time to get power
Power = 600 * 27^2 / 5.2 watts
divide by 1000 to get kw
Why did the sports car go on a diet? Because it wanted to accelerate its power game!
To calculate the average power developed by the sports car, we can use the formula:
Power = (force x distance) / time
However, we need to first find the force acting on the car. Using Newton's second law (Force = mass x acceleration), we can find the force as:
Force = mass x acceleration = 1200 kg x (27 m/s / 5.20 s)
Now, let's calculate the force:
Force = 1200 kg x (27 m/s / 5.20 s) = 6240 N
Next, let's calculate the distance traveled by the sports car during the acceleration. Since the initial velocity is 0 m/s, we can use the formula:
Distance = (1/2) x acceleration x time^2
Distance = (1/2) x (27 m/s) x (5.20 s)^2 = 357.42 m
Now, we can substitute the values back into the power formula:
Power = (force x distance) / time
Power = (6240 N x 357.42 m) / 5.20 s = 427745.38 W
So, the average power developed by the sports car is approximately 427745.38 watts.
If you prefer kilowatts, just divide the answer by 1000:
Power = 427745.38 W / 1000 = 427.75 kW
Therefore, the average power developed by the sports car is approximately 427.75 kilowatts.
To find the average power developed by the sports car, we will use the formula:
Power = work/time
First, we need to find the work done by the car. The work done is equal to the change in kinetic energy. The formula for kinetic energy is:
Kinetic energy = 1/2 * mass * velocity^2
The initial velocity of the car is 0 m/s, and the final velocity is 27.0 m/s. The mass of the car is 1200 kg.
Let's calculate the kinetic energy:
Kinetic energy = 1/2 * 1200 kg * (27.0 m/s)^2
Kinetic energy = 1/2 * 1200 kg * 729.0 m^2/s^2
Kinetic energy = 437,400 J
Next, we need to find the time it takes for the car to accelerate. The time given is 5.20 seconds.
Now, we can calculate the average power:
Power = work/time
Power = 437,400 J / 5.20 s
Power = 84,115.38 W
Therefore, the average power developed by the car is 84,115.38 watts.
To convert this to kilowatts, we divide by 1000:
Power in kilowatts = 84,115.38 W / 1000
Power in kilowatts = 84.12 kW
Therefore, the average power developed by the car is 84.12 kilowatts.
To calculate the average power developed by the sports car, you need to consider the work done on the car and the time it takes to do that work. The work done is given by the equation:
Work = force x distance
In this case, the force is the net force acting on the car, which is equal to the product of the car's mass and acceleration. The distance is the displacement of the car, which is the final velocity multiplied by the time taken.
Given:
Mass of the car (m) = 1200 kg
Initial velocity (u) = 0 m/s
Final velocity (v) = 27.0 m/s
Time taken (t) = 5.20 s
First, let's find the acceleration (a) using the equation of motion:
v = u + at
Rearranging the equation, we get:
a = (v - u) / t
= (27.0 m/s - 0 m/s) / 5.20 s
= 5.19 m/s²
Now that we have the acceleration, we can find the net force (F) acting on the car using Newton's second law:
F = ma
= 1200 kg x 5.19 m/s²
= 6228 N
Next, let's calculate the displacement (s):
s = (u + v) / 2 x t
= (0 m/s + 27.0 m/s) / 2 x 5.20 s
= 70.2 m
Now we can find the work done on the car:
Work = force x distance
= 6228 N x 70.2 m
= 436543.6 J (joules)
Finally, we can calculate the average power (P) developed by the car using the formula:
P = Work / time
= 436543.6 J / 5.20 s
= 83992.23 W (watts)
To convert watts to kilowatts, divide the value by 1000:
P (in kilowatts) = 83992.23 W / 1000
= 83.99 kW
Therefore, the average power developed by the sports car is 83.99 kilowatts.