Question

Alcohol consumption slows people's reaction times. In a controlled government test, it takes a certain driver t - 0.35 s to hit the brakes in a crisis when unimpaired and 12 1.05 s when drunk. If the car is initially traveling at v 87 km/h, how much farther does the car travel before the brakes are applied when the person is drunk than it travels when the person is sober? additional distance traveled TOOLS x10

Answer 1

Initial speed, $v=87km/h=24.17m/s$

final speed, $v_{f}=0m/s$

Unimpaired driver

$t_{1}=0.35s$

Use Formula $v=u+at$

$v_{f}=v+a_{1}t_{1}$

$0m/s=24.17m/s+a_{1}*0.35s$

${\color{Red} a_{1}=-69.06m/s^{2}}$

Use Formula $s=ut+1/2at^{2}$

$s_{1}=vt_{1}+1/2a_{1}t_{1}^{2}$

$s_{1}=24.17m/s*0.35s-1/2*69.06m/s^{2}*(0.35s)^{2}$

$s_{1}=24.17*0.35-0.5*69.06*0.35^{2}$

${\color{Red} s_{1}=4.23m}$

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Drunk driver

$t_{2}=1.05s$

Use Formula $v=u+at$

$v_{f}=v+a_{2}t_{2}$

$0m/s=24.17m/s+a_{2}*1.05s$

${\color{Red} a_{2}=-23.02m/s^{2}}$

Use Formula $s=ut+1/2at^{2}$

$s_{2}=vt_{2}+1/2a_{2}t_{2}^{2}$

$s_{2}=24.17m/s*1.05s-1/2*23.02m/s^{2}*(1.05s)^{2}$

$s_{2}=24.17*1.05-0.5*23.02*1.05^{2}$

${\color{Red} s_{2}=12.69m}$

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$s=s_{2}-s_{1}=12.69m-4.23m$

ANSWER: ${\color{Red} s=8.46m}$

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