A car (m = 770.0 kg) accelerates uniformly from rest up an inclined road which rises uniformly, to a height, h = 45.0 m. Find the average power the engine must deliver to reach a speed of 20.9 m/s at the top of the hill in 19.5 s(NEGLECT frictional losses: air and rolling, ...)
To find the average power the engine must deliver, we can use the work-energy principle and the definition of power.
First, let's find the work done by the car to reach the top of the hill. The work done (W) is equal to the change in mechanical energy (ΔE) of the car. In this case, the car is initially at rest, so its initial mechanical energy is zero. At the top of the hill, it has both kinetic energy (½mv^2) and potential energy (mgh).
ΔE = E_f - E_i
= (½mv_f^2 + mgh) - 0
= ½mv_f^2 + mgh
Given that the mass of the car (m) is 770.0 kg, the final velocity (v_f) is 20.9 m/s, and the height of the hill (h) is 45.0 m, we can substitute these values into the equation:
ΔE = ½(770.0 kg)(20.9 m/s)^2 + (770.0 kg)(9.8 m/s^2)(45.0 m)
Next, we need to find the time it takes for the car to reach the top of the hill. This is given as 19.5 s.
Now, we can calculate the average power (P) delivered by the engine using the formula:
P = ΔE / t
Substituting the values we have:
P = (½(770.0 kg)(20.9 m/s)^2 + (770.0 kg)(9.8 m/s^2)(45.0 m)) / 19.5 s
Simplifying the equation and calculating the result will give the average power the engine must deliver to reach a speed of 20.9 m/s at the top of the hill in 19.5 seconds.