Question

8.A motorist is travelling at 15 m/s when he sees a child run into the road. He brakes and

the car comes to rest in 0.75 s.

a) Draw a velocity time graph to show the deceleration, and use your graph to

calculate the distance travelled once the brakes are applied.

b) The deceleration of the car.

Answer 1

Explanation & Calculations

1). Velocity-time graph & consider the shown angle as $\small \theta$

Distance traveled is the area under the graph

$\qquad \begin{aligned} \small \text{Distance} &= \small \frac{1}{2}\times 0.75s \times15ms^{-1}\\ \small &= \small \bold{5.625m} \end{aligned}$

2). Acceleration is the slope (gradient) of the graph = $\small \tan\theta$ & can be found using trigonometric relationships for the triangle under the curve.

$\qquad \begin{aligned} \small \text{Acceleration} &= \small \tan\theta\\ \small \text{but} \tan(\pi-\theta) &= \frac{15ms^{-1}}{0.75s}\\ \small -\tan\theta &= \small 20ms^{-2}\\ \small \tan\theta &= \small \bold{-20ms^{-2}}\\ \small \text{Deceleration} &= \small \bold{20ms^{-2}} \end{aligned}$