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Topic: Distance Problem (Read 399 times) |
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ThudnBlunder
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Distance Problem
« on: Apr 22nd, 2003, 11:32am » |
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A car, initially at rest, accelerates up to a maximum speed of v, and then slows down to a stop again.
The graph of velocity against time (t seconds from start to stop) is a semicircle, as shown in the diagram below:
In order to find the total distance travelled, it is often useful to calculate the area under the curve.
One student claims that, since the radius of the semicircle is v, the distance travelled is (PI/2).v2, while another disagrees - saying that, as t is the diameter of the semicircle, the distance travelled is actually (PI/2).(t/2)2.
Which one is right?
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| « Last Edit: Apr 22nd, 2003, 11:33am by ThudnBlunder » |
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towr
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Re: Distance Problem
« Reply #1 on: Apr 22nd, 2003, 12:19pm » |
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Well, since it is a semicircle, v = t/2 (disregarding the units), so it doesn't matter.
Of course in the end you shouldn't diregard the units, so they're both wrong. It's (PI/2).(v.t/2)
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