2. A car of mass 1540 kg traveling at 28 m/s is at the foot of a hill that rises 125 m in 3.6 km. At the top of the hill, the speed of the car is 8 m/s. Find the average power delivered by the car's engine, neglecting any frictional losses.
A car of mass 1550 kg traveling at 24 m/s is at the foot of a hill that rises 125 m in 3.4 km. At the top of the hill, the speed of the car is 10 m/s. Find the average power delivered by the car's engine, neglecting any frictional losses
To find the average power delivered by the car's engine, we can use the work-energy principle. The work done by the engine is equal to the change in the car's kinetic energy.
First, let's find the initial kinetic energy of the car. The formula for kinetic energy is:
KE = (1/2) * mass * velocity^2
Substituting the given values:
Mass of the car (m) = 1540 kg
Initial velocity (vi) = 28 m/s
KE_initial = (1/2) * 1540 kg * (28 m/s)^2
Next, let's find the final kinetic energy of the car. At the top of the hill, the car's velocity is given as 8 m/s. So the final kinetic energy (KE_final) is:
KE_final = (1/2) * 1540 kg * (8 m/s)^2
Now, using the work-energy principle, the work done by the engine is equal to the change in kinetic energy:
Work_done = KE_final - KE_initial
Finally, to find the average power delivered by the car's engine, we divide the work done by the time taken. The time taken is the distance divided by the average velocity. The distance is given as 3.6 km, which is equal to 3600 m. The average velocity can be calculated by dividing the total change in position by the time taken:
Average_velocity = (change_in_position) / (time_taken)
Average_velocity = 125 m / (3600 m / 28 m/s)
With the average velocity calculated, we can now find the time taken (t):
t = (distance) / (average_velocity)
t = 3600 m / (average_velocity)
Now, we have all the required values to calculate the average power:
Average_power = Work_done / t
Substituting the values for work done and time taken, we can find the average power delivered by the car's engine.