First slide
Average velocity
Question

 A point moves with uniform acceleration and v1v2, and v3 denote the average velocities in the three successive intervals of time t1, t2 and t3. Which of the following relations is correct ?

Moderate
Solution

Suppose u be the initial velocity.
 Velocity after time t1 :v11=u+ at   Velocity after time t1+t2  : v22=u+at1+t2  Velocity after time t1+t2+t3:v33=u+at1+t2+t3  Now,  v1=u+v112=u+u+at12=u+12at1 v2=v11+v222=u+at1+12at2  v3=v22+v332=u+at1+at2+12at3  So  v1-v2=-12at1+t2 v2-v3=-12at2+t3 v1-v2:(v2-v3)=t1+t2:t2+t3

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