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einstein314
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Homework Statement
A particle moving from a point [itex] A [/itex] to a point [itex] B [/itex], [itex] 1 [/itex] meter away, travels in a straight line in such a way so that its acceleration is proportional to the distance left to point [itex] B [/itex]. If the particle arrives at point [itex] B [/itex] in [itex] 1 [/itex] second, how long did it take for the particle to reach the point halfway to point [itex] B [/itex]?
Homework Equations
I suppose we need that the acceleration is the second-derivative of position.
The Attempt at a Solution
So we know that [itex] a(t) = \frac{d^2p}{dt^2} = k(1 - p(t)) [/itex] (and [itex] a(1) = 0 [/itex] and [itex] p(0) = 0 [/itex] and [itex] p(1) = 1 [/itex]), but I don't know how to solve this differential equation. Once [itex] p(t) [/itex] is found, [itex] t [/itex] can be found by equating [itex] p(t) = \frac{1}{2} [/itex].
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