part 1
A 1760 kg car accelerates uniformly from rest to 8.8 m/s in 4.52 s. Find the work done on the car in this time.
Answer in units of J.
part 2
Find the average power delivered by the engine in the first 1.808 s.
Answer in units of W.
part 3
Find the instantaneous power delivered by the engine at t2 = 2.7572 s.
Answer in units of W.
Part 1:
To find the work done on the car, we need to use the work-energy principle. The work done on an object is equal to the change in its kinetic energy. The formula to calculate work is:
Work = (final kinetic energy) - (initial kinetic energy)
Given that the car starts from rest, its initial kinetic energy is zero. Therefore, the work done on the car is equal to its final kinetic energy.
To calculate the final kinetic energy, we use the formula:
Kinetic energy = (1/2) * mass * velocity^2
Where:
mass = 1760 kg (given)
velocity = 8.8 m/s (given)
Plugging in the values, we get:
Kinetic energy = (1/2) * 1760 kg * (8.8 m/s)^2
Simplifying the equation gives us:
Kinetic energy = 67802.4 J
Therefore, the work done on the car in this time is 67802.4 J.
Part 2:
To find the average power delivered by the engine in the first 1.808 s, we can use the formula for power:
Power = Work / time
We already know the work done on the car, which is 67802.4 J. The time given is 1.808 s.
Plugging in the values, we get:
Power = 67802.4 J / 1.808 s
Calculating this expression gives us:
Power ≈ 37496.69 W
Therefore, the average power delivered by the engine in the first 1.808 s is approximately 37496.69 W.
Part 3:
To find the instantaneous power delivered by the engine at t2 = 2.7572 s, we need to first determine the instantaneous acceleration of the car at that time.
We can use the formula:
Acceleration = (final velocity - initial velocity) / time
Given that the initial velocity is 0 m/s, the final velocity is 8.8 m/s (given), and the time is 2.7572 s, we substitute the values into the equation:
Acceleration = (8.8 m/s - 0 m/s) / 2.7572 s
Calculating this expression gives us the value of acceleration.
Once we have the acceleration, we can calculate the instantaneous power. The instantaneous power is given by:
Instantaneous power = force * velocity
Since force = mass * acceleration and velocity = final velocity, we can substitute the values into the equation:
Instantaneous power = (mass * acceleration) * (final velocity)
Substituting the given values of mass, acceleration, and final velocity, we can calculate the instantaneous power.