A 1000 kg sports car accelerates from 0 to 30 m/s in 10 s. What is the average power of the engine?
Well, if your sports car wants to win the race, it needs to flex its engine muscles! To find the average power of the engine, we can use the formula:
Power = Work/Time
First, let's find the work done by the car. We can use the equation:
Work = (1/2) * mass * velocity^2
Substituting the given values:
Work = (1/2) * 1000 kg * (30 m/s)^2
Work = 450,000 Joules
Now, since the time taken is 10 seconds:
Power = Work/Time
Power = 450,000 J/10 s
Power = 45,000 Watts
So, the average power of the engine is 45,000 Watts. That's a lot of horsepower! Those pistons are definitely pumping hard to get the car moving.
To determine the average power of the engine, we can use the formula:
Power = (force × distance) ÷ time
First, let's calculate the force acting on the car using Newton's second law:
force = mass × acceleration
Given:
mass (m) = 1000 kg
acceleration (a) = change in velocity ÷ time taken = (30 m/s - 0 m/s) ÷ 10 s = 3 m/s²
force = 1000 kg × 3 m/s² = 3000 N
Next, we need to find the distance traveled by the car during acceleration. We can use the formula:
distance = (initial velocity × time) + (0.5 × acceleration × time²)
Given:
initial velocity (u) = 0 m/s
time (t) = 10 s
acceleration (a) = 3 m/s²
distance = (0 m/s × 10 s) + (0.5 × 3 m/s² × (10 s)²)
distance = 0 + 0.5 × 3 m/s² × 100 s²
distance = 0.5 × 3 m/s² × 100 s²
distance = 150 m
Now, let's calculate the average power:
Power = (force × distance) ÷ time
Power = (3000 N × 150 m) ÷ 10 s
Power = 450000 Nm/s ÷ 10 s
Power = 45000 W
Therefore, the average power of the engine is 45000 watts.
To find the average power of the engine, we can use the formula:
Average Power = Work Done / Time
First, let's find out the work done by the engine. The work done is equal to the change in kinetic energy of the car.
The change in kinetic energy can be calculated using the formula:
Change in Kinetic Energy = (1/2) * mass * (final velocity^2 - initial velocity^2)
Given:
Mass of the car (m) = 1000 kg
Initial velocity (u) = 0 m/s
Final velocity (v) = 30 m/s
Using these values, we can calculate the change in kinetic energy as follows:
Change in Kinetic Energy = (1/2) * 1000 kg * (30 m/s)^2
Next, we need to calculate the average power by dividing the change in kinetic energy by the time taken.
Given:
Time taken (t) = 10 s
Using the formula:
Average Power = Change in Kinetic Energy / Time taken
Substituting the values, we get:
Average Power = [(1/2) * 1000 kg * (30 m/s)^2] / 10 s
Simplifying the equation further:
Average Power = (1/2) * 1000 kg * (30 m/s)^2 / 10 s
Average Power = 150000 watts
Therefore, the average power of the engine is 150,000 watts.
Power is work done per unit time.
Average power is increase in work/energy divided by the duration for the increase.
initial kinetic energy, Ei = 0
final kinetic energy, Ef
= (1/2)mv²
= (1/2)1000 30² kg-m²-s-2
duration, t = 10 s
Average power
= (Ef-Ei)/t
= 45,000 W (or joules-s-1