Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line

Kinematics of motion in a straight line — practice question

A car moves in a straight line from $A$ to $B$, covering $12\,\text{km}$ in $552$ seconds. It begins at rest at $A$ and speeds up for $T_1\,\text{s}$ with acceleration $0.3\,\text{m s}^{-2}$, reaching speed $V\,\text{m s}^{-1}$. It then travels at constant speed $V\,\text{m s}^{-1}$ for $T_2\,\text{s}$. After that, it slows down for $T_3\,\text{s}$ at $1\,\text{m s}^{-2}$, stopping at $B$.
(i)[3]

Draw the velocity-time graph for the journey and write $T_1$ and $T_3$ in terms of $V$.

(ii)[5]

Write the total distance travelled in terms of $V$ and show that $13V^2 - 3312V + 72000 = 0$. Hence determine $V$.

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