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
Expert's answer
2020-05-05T18:44:24-0400

Explanation & Calculations


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




Distance traveled is the area under the graph

Distance=12×0.75s×15ms1=5.625m\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 = tanθ\small \tan\theta & can be found using trigonometric relationships for the triangle under the curve.

Acceleration=tanθbuttan(πθ)=15ms10.75stanθ=20ms2tanθ=20ms2Deceleration=20ms2\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}



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!

Comments

No comments. Be the first!

Leave a comment