Motion in a straight line
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A particle moves along a straight line such that its position vector \(r(t) \text{ cm}\), at time \(t\) seconds is given by \(r(t)=\left(4 t-t^2\right) i\), for \(t \geq 0\). Find:
i) \(\dot{r}(t)\)
ii) The velocity of the particle when \(t=3\) seconds.
iii) When and where the particle changes direction.
iv) The distance travelled in the first \(6\) seconds.
i) \((4-2 t) i \text{ cm} / \text{s}\)
ii) \(-2 i \text{ cm} / \text{s}\)
iii) The particle changes direction when \(t=2\)
iv) \(20 \text{ cm}\)
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