Question #113155

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.

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.

Expert's answer

**Explanation & Calculations**

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

Distance traveled is the area under the graph

"\\qquad \n\\begin{aligned}\n\\small \\text{Distance} &= \\small \\frac{1}{2}\\times 0.75s \\times15ms^{-1}\\\\\n\\small &= \\small \\bold{5.625m}\n\\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 \n\\begin{aligned}\n\\small \\text{Acceleration} &= \\small \\tan\\theta\\\\\n\\small \\text{but} \\tan(\\pi-\\theta) &= \\frac{15ms^{-1}}{0.75s}\\\\\n\\small -\\tan\\theta &= \\small 20ms^{-2}\\\\\n\\small \\tan\\theta &= \\small \\bold{-20ms^{-2}}\\\\\n\\small \\text{Deceleration} &= \\small \\bold{20ms^{-2}}\n\\end{aligned}"

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