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First Equation of Motion

A particle mo...

Question

A particle moves with constant acceleration. If v1, v2 and v3 are the three average velocities in three successive intervals t1, t2 and t3 of time, prove that: v1-v2/v2-v3=t1+t2/t2+t3.

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Solution

Dear Student,
Assume the particles moves the separation AB, BC and CD in time t1,t2 and t3 individually.
Speed at B = u+at1

Speed at C = u+a(t1+t2)

Speed at D = u + a( t1+t2+t3)

Average speed (v1)=( Initial Velocity + Final Velocity )/2

= (u + u + at1)/2
= u+1/2 at1

V2 = u+at1+1/2at2

V3 = u+ at1+at2+1/2at3

There fore we get

V1-V2 = -at1/2-at2/2
V2-V3 = -at2/2-at3/2

dividing we get ( t1+t2 ) / ( t2 + t3 )

(V1-V2)/(V2-V3) = (t1+t2)/(t2+t3)
Hence proved.

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