Mr Chan was driving a car along a straight road. He was $35$ m away from the stop line when he app

Question

Mr Chan was driving a car along a straight road. He was $35$ m away from the stop line when he applied his brakes near a traffic light. His acceleration, $a$ $\text{m/s}^2$, after applying the brakes was given by $a = -7.5\mathrm{e}^{-\frac{t}{2}}$, where $t$ is the time in seconds after he applied the brakes. Explain mathematically why $a < 0$ for all $t \ge 0$ and the significance of $a < 0$.[2] Mr Chan’s car was travelling at $14$ m/s just before he applied his brakes. Express the velocity of his car, $\mathrm{v}$ m/s, in terms of $t$.[3] Hence find the time taken for his car to come to a complete stop.[2] Obtain an expression, in terms of $t$, for the displacement of Mr Chan’s car from the point he applied the brakes.[3] Determine if Mr Chan’s car was able to come to a complete stop before reaching the stop line. Explain your answer.[2]

Accepted Answer

(b) $\mathrm{v} = 15\mathrm{e}^{-\frac{t}{2}} - 1$ (c) $5.42$ s (d) $ \mathrm{s} = -30 \mathrm{e}^{-\frac{t}{2}} - t + 30$

2024 CGSS P2 Q9

2024 CGSS P2 Q9