A car (m = 640.0 kg) accelerates uniformly from rest up an inclined road which rises uniformly, to a height, h = 43.0 m. Find the average power the engine must deliver to reach a speed of 19.9 m/s at the top of the hill in 23.9 s(NEGLECT frictional losses: air and rolling, ...)
power * time = work done = m g h + (1/2) m v^2
16598.09 watt
To find the average power the engine must deliver, we need to calculate the work done by the car and divide it by the time it takes to reach the top of the hill.
First, let's calculate the work done by the car. The work done by a force is given by the equation:
Work = Force * Distance * cos(θ)
In this case, the force is the component of the car's weight parallel to the incline, the distance is the height of the hill (h = 43.0 m), and θ is the angle of the incline.
The weight of the car, W, is given by:
W = m * g
where m is the mass of the car (640.0 kg) and g is the acceleration due to gravity (9.8 m/s²).
Next, we need to calculate the angle of the incline, θ. We can use trigonometry to find the angle:
θ = arctan(h / distance)
In this case, the distance is not given. However, we can use the time and the final velocity of the car to find the distance traveled.
The average velocity of the car is given by:
v_avg = (v_0 + v_f) / 2
where v_0 is the initial velocity (0 m/s) and v_f is the final velocity (19.9 m/s).
Using the equation for average velocity, we can find the distance traveled by the car:
distance = v_avg * time
where time is given as 23.9 s.
Now, we have all the information we need to calculate the work done by the car. We can plug in the values into the equations:
W = m * g * distance * cos(θ)
Finally, we can find the average power delivered by the engine:
Average Power = Work / time