107 149
Assignments Done
100%
Successfully Done
In January 2023

# Answer to Question #113155 in Mechanics | Relativity for Mateus Michael Ndinomwene

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.
1
2020-05-05T18:44:24-0400

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}"

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!