The motorist

Classical Mechanics Level 2

A motorist travelling at 13 ms − 1 13 \text{ ms}^{-1} approaches a traffic light which turns red when he is 25 m 25\text m away from the stop line. His reaction time (i.e. the interval between seeing the red line and applying the brakes) is 0.7 s 0.7\text s and the condition of the road and his tyres are such that the car cannot slow down at a rate of more than 4.5 ms − 2 4.5 \text{ ms}^{-2} . If he brakes fully, how far from the stop line will he stop, and on which side of it?

2.9 m beyond the line 2.9 m behind the line 4.0m behind the line 4.0m beyond the line

Wee Xian Bin by Wee Xian Bin , 25, Singapore

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1 solution

Wee Xian Bin
Jun 28, 2016

v 2 = u 2 + 2 a s v^2 = u^2 + 2as

0 2 = ( + 13 ) 2 + 2 ( − 4.5 ) s 0^2 =(+13)^2 + 2(-4.5)s

s = 18.78 s = 18.78 m

Before breaking: s = u t = ( + 13 ) ( 0.7 ) = 9.1 s=ut=(+13)(0.7) = 9.1 m

Total distance = 9.1 + 18.78 - 25 = 2.9 m beyond the line.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice question.

Ashish Menon - 4 years, 11 months ago

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