time, force, distance, acceleration

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.

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?

Re: time, force, distance, acceleration

Quote:

Originally Posted by

**furor celtica** 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.

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?

Non-constant acceleration. Your first calculation does not assume constant acceleration while the second does.

CB