Answer to Question #308947 in Mechanics | Relativity for Felicia Sandoval

Question

The speed limit in a school zone is 40 km/hr. A driver traveling at this speed sees a child run onto the road 13 m ahead of his car. He applies the brakes, and the car decelerates at a uniform rate of 8 m/s². If the driver’s reaction time is 0.25 s, will the car stop before hitting the car?

Answer 1

Explanations & Calculations

$\qquad\qquad \begin{aligned} \small 40\,kmh^{-1} &=\small 11.11\,ms^{-1} \end{aligned}$

• The distance travelled during the reaction time

$\qquad\qquad \begin{aligned} \small d&=\small ut = 11.11\,ms^{-1}\times 0.25\,s = 2.78\,m \end{aligned}$

• Then the distance remained to stop the car at the stated deceleration is

$\qquad\qquad \begin{aligned} \small S = 13\,m-2.78\,m = 10.22\,m \end{aligned}$

• But the distance the car would travel during deceleration is

$\qquad\qquad \begin{aligned} \small v^2 &=\small u^2 +2as\\ \small 0&=\small (11.11\,ms^{-1})^2 +2(-8\,ms^{-2})\times S_1\\ \small S_1 &=\small 7.7\,m \end{aligned}$

• Since the stopping distance is less than the actual remaining distance, the car stops before hitting.