A train starts at a station and stops at another station First the velocity of the train increases at - Physics - Kinematics

Question

A train starts at a station and stops at another station First the
velocity of the train increases at a uniform rate, reaches a
maximum velocity v and then starts decreasing at a constant rate If
the time spent for the entire journey is t, prove that the distance
between the entire station is 1/2vt

Manoj Singh · Accepted Answer

Dear Student,

Velocity increases or decreases with uniform rates so acceleration
constant during motion Therefore we can apply newton's
equations
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"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_57dfceb0ccb25%20png"
style="width: 300px; height: 126px;">

So for entire journey
S=  12at2                    
(1)Now for AC journeya = dvdt = v-0t'x = 12at'2 = vt'2  
(1)and v2 = 2a(S-x)(S-x) 2vt''= v2 ⇒vt''2 = S-x    
(2)Add eqution 1 and 2S = 12v(t'+t'') = 12vt