You are driving to the grocery store at 20m/s. You are 120 m from anintersection

Question

You are driving to the grocery store at 20m/s. You are 120 m from anintersection when the traffic light turns red. Assume that yourreaction time is 0.50 s and that your car brakes with constantacceleration. (a) How far are you from the intersection whenyou begin to apply the brakes?
1 ____ m
(b) What acceleration (magnitude) will bring you to rest right atthe intersection?
2 ____ m/s2
(c) How long (total) does it take you to stop?
3 ____ s (a) How far are you from the intersection whenyou begin to apply the brakes?
1 ____ m
(b) What acceleration (magnitude) will bring you to rest right atthe intersection?
2 ____ m/s2
(c) How long (total) does it take you to stop?
3 ____ s

Explanation / Answer

(a) How far are you from the intersection whenyou begin to apply the brakes?
1 ____ m
as the reaction time is 0.5sec the distance traveled during thereaction time=0.5*20=10m
hence distance remaining when brakes are applied =120-10=110m
(b) What acceleration (magnitude) will bring you to rest right atthe intersection?
2 ____ m/s2
s=110m
u=20m/sec
v=0m/sec
so usingv2=u2+2as
0=400+2a*110
so acceleration= -1.8181m/sec2
(c) How long(total) does it take you to stop?
3 ____ s
time=[v-u]/a=[0-20]/-1.8181=11.00sec

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