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Math Help - time, force, distance, acceleration

  1. #1
    Senior Member furor celtica's Avatar
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    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?
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  2. #2
    Grand Panjandrum
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    Re: time, force, distance, acceleration

    Quote Originally Posted by furor celtica View Post
    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
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