A car with a mass of 1200 kg kg starts from
rest and accelerates to a speed of 12 m/s in
12.2 s. Assume that the force of resistance
remains constant at 328 N during this time.
What is the average power developed by
the car’s engine?
Answer in units of W.
1/2 m vf^2+328*distance=work done
but distance=avgspeed*time=12/2*12.2
so calculate work done. Now divide by time, and you have power.
To find the average power developed by the car's engine, we can use the formula:
Average Power = Work / Time
To determine the work done by the car, we need to calculate the net force acting on it and the distance it travels.
First, let's determine the net force acting on the car. The net force is the difference between the force applied by the engine and the force of resistance:
Net Force = Force Applied - Force of Resistance
The force applied by the engine can be calculated using Newton's second law:
Force Applied = Mass x Acceleration
Given that the mass of the car is 1200 kg and the time taken to reach the speed of 12 m/s is 12.2 s, we can find the acceleration using the formula:
Acceleration = Change in Velocity / Time
Change in Velocity = Final Velocity - Initial Velocity
= 12 m/s - 0 m/s (since the car starts from rest)
Substituting the values, we have:
Change in Velocity = 12 m/s
Acceleration = 12 m/s / 12.2 s
Next, we can calculate the force applied by the engine:
Force Applied = 1200 kg x 12 m/s / 12.2 s
Now, let's calculate the net force:
Net Force = Force Applied - Force of Resistance
= (1200 kg x 12 m/s / 12.2 s) - 328 N
With the net force determined, we can calculate the work done by the car. The work done is equal to the force applied multiplied by the distance traveled. As the car starts from rest and accelerates to a given velocity, we need to find the distance traveled during this time. We can use the formula:
Distance = Initial Velocity x Time + (1/2) x Acceleration x Time^2
Given that the initial velocity is 0 m/s, the distance traveled can be calculated as:
Distance = 0 m/s x 12.2 s + (1/2) x Acceleration x (12.2 s)^2
Finally, we can calculate the work done:
Work = Net Force x Distance
Having the work done and the time, we can now find the average power developed by the car's engine using the formula mentioned earlier:
Average Power = Work / Time
Calculating all the values and applying the formula will give the answer in watts (W).