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

Question #308947

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?




1
Expert's answer
2022-03-10T18:01:19-0500

Explanations & Calculations


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

  • The distance travelled during the reaction time

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

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

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

  • But the distance the car would travel during deceleration is

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


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

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