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Inequality help

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dekoyl:
A particle is moving in a straight line and its displacement from the origin at any time is given by . In the time interval find when .

At first I had:


But I couldn't extract the right answers from that. However, when I had:



I could get the answers.

Is there an explanation for which method to use? I think I encountered something like this in methods whereby some solutions would be missing if I factorised a specific way.

The answer is except . Thanks a lot. :)

humph:

--- Quote from: dekoyl on July 15, 2009, 04:13:28 pm ---A particle is moving in a straight line and its displacement from the origin at any time is given by . In the time interval find when .

At first I had:


But I couldn't extract the right answers from that. However, when I had:



I could get the answers.

Is there an explanation for which method to use? I think I encountered something like this in methods whereby some solutions would be missing if I factorised a specific way.

The answer is except . Thanks a lot. :)

--- End quote ---



Thus when
(1) and ,
OR
(2) and .
Note that is impossible, so we only need to consider case (2). In this case, we are left with the conditions and . The first condition implies that , and the second condition implies that .

Best way to solve this type of question is to factorise and have an inequality of the form , and then consider the possible combinations of or for which this inequality holds (so more of a combinatorial argument).

TrueTears:
Well when I first saw the equation I thought of subbing u = cos(t) straight away because that way you can get a quadratic.

Although by looking at your first method I don't see how you can solve for t after you get . What's the next step?

So I just did substitution.

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