A particle $P$ moves in a straight line so that $t$ seconds after leaving a fixed point \(O

Question

A particle $P$ moves in a straight line so that $t$ seconds after leaving a fixed point $O$, its velocity $v$ ms${}^{-1}$ is given by $v = (2t - 3)^2 - 9$. Sketch the $v - t$ graph of the particle $P$ for $0 \le t \le 5$. Hence or otherwise, find the range of values of $t$ for which the acceleration of $P$ is less than $4$ m/$\mathrm{s}^2$. find the distance travelled by $P$ in the first $5$ seconds.

Accepted Answer

(a) Upward-opening $v-t$ parabola through $(0,0)$ and $(3,0)$, with vertex $ \left(\frac{3}{2},-9 \right)$ and endpoint $(5,40)$. (b) (i) $0 \leq t < 2$ s; (ii) $\frac{158}{3}$ m

Kinematics - Interpreting and Sketching Motion Graphs

Kinematics - Interpreting and Sketching Motion Graphs

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