Question

A point moves with uniform acceleration $v_1,v_2$ and $v_3$ denote the average velocities in three successive intervals of time $t_1, t_2$ and $ t_3 $. Correct relation among the following is

• 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. $(v_1 -v_2 ):(v_2 -v_3 ) = ( t_1 - t_2) : (t_2 + t_3)$
• D. $(v_1 -v_2 ):(v_2 -v_3 ) = ( t_1 +t_2) : (t_2 -t_3)$

Answer 1

Answer: (B)

$V_{avg} = \frac{ut + \frac{1}{2} at^2}{t} = u + \frac{1}{2} at$
$\nu_1 = u + \frac{1}{2} at_1$ ........(1)
$\nu_2 = \nu_1 + \frac{1}{2} at_2$ .......(2)
$\nu_3 = \nu_2 + \frac{1}{2} at_3$ .......(3)