Same physics question, quick fix please answer

Question

Need help answering P2, i know the answer to part 1. Im unsure how I work out P2.

I got 21271.92W as my answer, because it is a car and my answer is in watts, does that mean it is incorrect.
A car of mass 1.5 tonnes is driving up a hill, the hill makes an angle of 10 degrees to the
horizontal, at a constant 30km/h.

P1- Neglecting any friction, what is the power required from
the engine to drive the car up the hill under these conditions?

P2 -If the car takes 20 seconds to climb the hill, how much energy will the journey consume? If
the car now doubles its speed and so ascends the hill in just 10 seconds, how much
energy will the journey have consumed?

Answer 1

P = Fv

 

F = mg sinθ

 

v = 30 km/h = 30,000 m / (3600 s) ≅ 8.333 m/s

 

θ = 10º

 

m = 1.5 tonnes = 1500 kg

 

F = (1500 kg)(9.8 m/s²)sin10° = 2552.6 N

 

P = Fv = (2552.6 N)(8.333 m/s) = 21,270.8 W  [same as your answer, except slightly different roundoff]

 

E = Pt

 

First part of part 2:

 

E = Pt = (21,270.8 W)(20 s) = 425,416 J

 

Second part of part 2:

 

v' = 2v

t' = t/2

F' = F

P' = F'v' = F(2v) = 2Fv = 2P

 

E' = P't' = (2P)(t/2) = Pt = E = 425,416 J

 

This makes sense to get the same energy, since the work done depends only on the start and end points, not on how you got from the start to the end point.