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The position of a particle moving along ...

The position of a particle moving along x-axis varies eith time t as `x=4t-t^(2)+1`. Find the time interval(s) during which the particle is moving along positive x-direction.

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To solve the problem, we need to determine the time intervals during which the particle is moving in the positive x-direction. We start with the given position function: \[ x(t) = 4t - t^2 + 1 \] ### Step 1: Find the velocity function The velocity \( v(t) \) of the particle is the derivative of the position function with respect to time \( t \): \[ ...
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