# Homework Help: Time, force, distance, acceleration

1. Sep 12, 2011

### furor celtica

1. The problem statement, all variables and given/known data

A car of mass 1220 kg travels up a straight road which is inclined at an angle A to the horizontal, where sinA=0.05. The resistances to motion are modelled as a constant force of magnitude 1400 N. The car travels a distance of 25.8 metres whilst increasing its speed from 8ms^-1, at the point X, to 12 ms^-1 at the point Y. Calculate the work done by the car's engine in travelling from X to Y.
The car's engine works at a constant rate of 40 kW. Calculate the time taken to travel from X to Y.

2. Relevant equations

3. The attempt at a solution
For the first problem I got 100 658 watts, which is correct.
However I'm confused by the second.

Firstly I can use power= work/time to get time=100 658/40 000= 2.51645 seconds
But I can also use s=0.5(u+v)t to get time= (2x25.8)/(12+8)= 2.58 seconds
Where have I gone wrong?

2. Sep 12, 2011

### Delphi51

Your calcs check out. It sure looked like an inconsistency in the given numbers but .....
Constant power implies that the car will not accelerate constantly because part of the power is proportional to velocity, P = F*v. The formula s=0.5(u+v)t only works for constant acceleration.

3. Sep 12, 2011

### vela

Staff Emeritus
The answer should be in joules, not watts.
You're assuming the acceleration is constant, but it isn't. Remember that $P = \vec{F}\cdot\vec{v}$. If P is constant, as the car speeds up, F must decrease, so the car's acceleration is decreasing.

4. Sep 13, 2011