A car starts from rest, and begins accelerating at a constant rate sigma_1. It a

Question

A car starts from rest, and begins accelerating at a constant rate sigma_1. It accelerates at this rate for a distance of G ___ m from its starting point, and then immediately begins to decelerate at a different constant rate sigma_2, eventually coming to rest again after traveling an additional distance of H. ___ m from where it began decelerating. The entire trip from start to finish (starting and ending at rest) lasts for a duration of I. ___ What is the duration of the first part of the trip (the acceleration phase)? What is the duration of the second part of the trip (the deceleration phase)? What is the car's average speed over the course of the entire trip?

Explanation / Answer

As we know that

(a)

t1 = Duration of first part of the trip

s = (u*t1) + (0.5*a1*t1)^2

30.2 = (0.5*a1*t1)^2

(60.4/a1)^0.5 = t1

(b)

Duration of second part of the trip = t2

As we know that

v^2 = u^2 - 2*a*s

u^2 = 2*a*s

u^2 = 2*a2*40.5

u = (81*a2)^0.5

v = u - a2*t2

(81*a2)^0.5 = a2*t2

t2 = (81/a2)^0.5

(c)

As we know that

average speed = Total distance / total time

average speed = (30.2+40.5) / 28

average speed = 70.7/28 = 2.525 m/s

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