Answer to Question #113906 in Mechanics | Relativity for Mateus Michael Ndinomwene

Question

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 [4]
b) The deceleration of the car.

Answer 1

Due to the constant deceleration, the velocity decreases linearly over time. Let $V_0$ be the initial velocity and $a$ be the deceleration. Since the velocity decreases, $a$ is negative. We may write the formula for velocity $V(t) = V_0 + at$ .

(a) At the end of moving the velocity is equal to 0. The displacement of motorist is the area under the curve representing the dependence of velocity on time. This area is the area of a triangle, so we may write the expression

$S=\dfrac12\cdot V_0\cdot t = \dfrac12\cdot15\,m/s\cdot0.75\,s = 5.625\,m$ .

(b) Let us calculate the deceleration. $V(0.75) = 0\,m/s, \;\; V(0.75) = 15\,m/s+ a\cdot0.75\,s,$ so

$a = \dfrac{0\,m/s-15\,m/s}{0.75\,s} = -20\, m/s^2.$