What is the answer to this?

Question

A car moves along an x axis through a distance of 980 m, starting at rest (at x = 0) and ending at rest (at x = 980 m). Through the first 1/4 of that distance, its acceleration is +5.25 m/s2. Through the next 3/4 of that distance, its acceleration is -1.75 m/s2. What are (a) its travel time through the 980 m and (b) its maximum speed?

Answer 1

Compute the individual times as
d=.5*a*t^2


a= acceleration.

This problem is commonly called "piece-wise linear", in that the laws of motion are linear in the segments as described.

from the problem statement there are two segments:

980/4=.5*5.25*t1^2
t1=sqrt(980/(4*.5*5.25))
=9.661s

the max velocity will be the velocity at
9.661 s

It will also be the initial velocity for the second segment, so let's compute it now:

from the equation
v=a*t
v=5.25*9.661
=50.72 m/s

for the second segment
3*980/4=50.72*t-.5*1.75*t^2

t=28.98 s

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