As you drive your car along a country road at night, a deer jumps out of the woo

Question

As you drive your car along a country road at night, a deer jumps out of the woods and stands in the middle of the road ahead of you. This occurs just as you are passing from a 55-mi/h zone to a 50-mi/h zone. At the 50-mi/h speed-limit sign, you slam on the car's brakes, causing them to lock up, and skid to a stop inches from the startled deer. As you breathe a sigh of relief, you hear the sound of a police siren. The policeman proceeds to write you a ticket for driving 56 mi/h in 50-mi/h zone. Because of your preparation in physics, you are able to use the 32.5-m-long skid marks that your car left behind as evidence that you were not speeding. Based on your evidence, at what speed were you actually driving? (The coefficient of friction between between automobile tires and dry concrete is 0.80.)
mi/h

Explanation / Answer

assume the decleration is a

mg = ma

a = g              (1)

assume the speed was v

0 = v - at

t = v /a

s = vt - 1/2 a t2 = v (v/a) - (1/2)a (v/a)2

= v2 / 2a

so

v = sqrt (2as) = sqrt(2*g*s) = sqrt(2*0.80*9.8*32.5) = 22.574 m/s

= 22.574 (m/s) *(1 mile/1609m) * (3600 s/1 hr) = 50.5 mi/hr

speed was 50.5 mi/hr

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