A motorist suddenly notices a stalled car and slams on the brakes, negatively ac

Question

A motorist suddenly notices a stalled car and slams on the brakes, negatively accelerating at 6.2 . Unfortunately this isn't enough, and a collision ensues. From the damage sustained, police estimate that the car was going 16 at the time of the collision. They also measure skid marks 36 long. Express your answer to two significant figures and include the appropriate units. (a) How fast was the motorist going when the brakes were first applied? (b) How much time elapsed from the initial braking to the collision? Thank you

Explanation / Answer

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(a) The initial speed of the car was :

v² = v² + 2ax

Solve for initial velocity, v:

v² = v² - 2ax
= (5.6m/s)² - 2(-6.3m/s²)(29m)--->20km/h = 5.6m/s
= 19m/s

(b) Now, the time from braking to collision is :

v = v + at
t = (v - v) / a
= (5.6m/s - 19m/s) / -6.3m/s²)
= 2.1s

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