A point moves with uniform acceleration and v1, v2 and v3 denote the average velocities in the three successive intervals of time t1 , t2 and t3. Which of the following relation is correct?

A
$(v_{1} - v_{2}) : (v_{2} - v_{3}) = (t_{1} - t_{2}) : (t_{2} + t_{3})$
B
$(v_{1} - v_{2}) : (v_{2} - v_{3}) = (t_{1} + t_{2}) : (t_{2} + t_{3})$
C
$(v_{1} - v_{2}) : (v_{2} - v_{3}) = (t_{1} - t_{2}) : (t_{1} - t_{3})$
D
$(v_{1} - v_{2}) : (v_{2} - v_{3}) = (t_{1} - t_{2}) : (t_{2} - t_{3})$

Solution:

Average velocity in uniformly accelerated motion is given by,

$v_{a v} = \frac{s}{t} = \frac{u t + \frac{1}{2} a t^{2}}{t} = u + \frac{1}{2} a t N o w, v_{1} = u + \frac{1}{2} a t_{1} v_{2} = (u + a t_{1}) + \frac{1}{2} a t_{2} a n d v_{3} = u + a (t_{1} + t_{2}) + \frac{1}{2} a t_{3} ∴ (v_{1} - v_{2}) : (v_{2} - v_{3}) = (t_{1} + t_{2}) : (t_{2} + t_{3})$