Question 1184351
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Find the time it takes to travel 30km for a bus which accelerates uniformly 
from 40km/hr to 80km/hr. Show your solution.
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<pre>
You are given:  initial velocity  {{{v[1]}}} = 40 km/h;
                ending  velocity  {{{v[2]}}} = 80 km/h;

                travel distance   d = 30 km.


To find the time, start from these two kinematic equations


    d = {{{v[1]*t}}} + {{{(a*t^2)/2}}},      (1)

    a = {{{(v[2]-v[1])/t}}},            (2)


where " a " is the acceleration.  Substitute (2) into (1), eliminating "a".  You will get


    d = {{{v[1]*t + ((v[2]-v[1])/(2t))*t^2}}} = {{{v[1]*t + ((v[2]-v[1])/2)*t}}} = {{{v[1]*t + (v[2]*t)/2 - (v[1]*t)/2}}} = {{{(v[1]*t)/2 + (v[2]*t)/2}}} = {{{((v[1]+v[2])/2)*t}}}.


Thus you started from the formal kinematic formula (1)  and ended with intuitively understandable formula


    d = {{{((v[1]+v[2])/2)*t}}}.


Now you only need substitute the given data to get simple equation


    30 = {{{((40+80)/2)*t}}}

    30 = 60t

     t = {{{30/60}}} = {{{1/2}}}  of an hour = 30 minutes.    <U>ANSWER</U>
</pre>

Solved.