A car is traveling along a road at a uniform velocity when at time zero the driv

Question

A car is traveling along a road at a uniform velocity when at time zero the driver recognizes a hazard. At a moment 0.8 seconds later the driver brakes her vehicle , resulting in her vehicle sliding 90 ft in the same direction, at which time it strikes another stationary vehicle at 25 mph. The road surface is dry with a coefficient of friction of 0.75. The driver was traveling on a rural highway having a speed limit of 55 mph. Was she exceeding the speed limit? (Note: 5,280 ft = 1 mile, and g = 32.2 ft/s2)

Explanation / Answer

Let the speed of car be, v0 mph
Distance travelled by car in 0.8 sec = 0.8v ft
V 2= V02 - 2 x a x s

V= 25 mph

s = 90 ft = 0.0170 miles

g= 32.2 ft/s2 =[ 32.2 x (3600)2 / 5280 ] miles/ hr2

= 79036.36 miles/ hr2

a = 0.75 x g = 59277.7

252 = V02 - 2 x 59277.7 x 0.0170

625 + 2015.42 = V02

V0= 51.38 mph (Ans)

She was NOT exceedind the limit of 55 mph

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