Question

A particle is moving in a straight line with constant acceleration is initial velocity is you not if its velocity after a certain time interval is to you not successfully after that and in double that interval its velocity is how much

Answer 1

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)  

Normal speed (v1)=( starting +final)/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)/(V2-V3) = (t1+t2)/(t2+t3)

Hence proved.