B. If you brake hard and fast, you can bring a typical car to rest from 100 kph

Question

B. If you brake hard and fast, you can bring a typical car to rest from 100 kph (about 60 mph) in 5 seconds.
B.1 Calculate the magnitude of your acceleration, a0, assuming that it is constant.  m/s2

Why did we put a minus sign in front?

B.2 Suppose the car ahead of you (which was also going 100 kph) begins to brake with an acceleration a0 from B1. How far will he travel before he comes to a stop? (Hint: How much time will it take him to stop?)  m

B.3 What will be his average velocity over this time interval?  m/s

Explanation / Answer

B1: v0 = 100 kph = 100 x 1000 m / 3600 s

v0 = 27.78 m/s

vf = 0

t = 5 sec

vf = v0 + a t

0 = 27.78 + 5 a

a = - 5.56 m/s^2 .........Ans

minus sign because acceleration is in opposite direction as of velocity.

B2: 0^2 - 27.78^2 = 2(-5.56)(d)

d = 69.4 m

B3: average velocity = displacement / t

= 69.4 / 5

= 13.9 m/s

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