A particle moves with constant acceleration, let $v_1, v_2, v_3$ be the Average velocities in successive time interval $t_1, t_2$ and $t_3$ then
$\frac{{{v_1}\, - \,{v_2}}}{{{v_2}\, - \,{v_3}}}\, = \,\frac{{{t_1}\, - {t_2}}}{{{t_1}\, + \,{t_2}}}$
$\frac{{{v_1}\, - \,{v_2}}}{{{v_2}\, - \,{v_3}}}\, = \,\frac{{{t_1}\, - {t_2}}}{{{t_1}\, - \,{t_3}}}$
$\frac{{{v_1}\, - \,{v_2}}}{{{v_2}\, - \,{v_3}}}\, = \,\frac{{{t_1}\, + {t_2}}}{{{t_2}\, + \,{t_3}}}$
$\frac{{{v_1}\, - \,{v_2}}}{{{v_2}\, - \,{v_3}}}\, = \,\frac{{{t_1}\, - {t_2}}}{{{t_2}\, - \,{t_3}}}$
The two ends of a train moving with constant acceleration pass a certain point with velocities $u$ and $3 u$. The velocity with which the middle point of the train passes the same point is ........... $u$
A wheel of radius $1$ meter rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is
A body travels for $15\, sec$ starting from rest with constant acceleration. If it travels distances ${S_1},\;{S_2}$ and ${S_3}$ in the first five seconds, second five seconds and next five seconds respectively the relation between ${S_1},\;{S_2}$ and ${S_3}$ is
A particle is projected vertically upwards from a point $A$ on the ground. It takes $t_1$ time to reach a point $B$ but it still continues to move up. If it takes further $t_2$ time to reach the ground from point B then height of point $B$ from the ground is
The displacement $x$ of a particle varies with time $t$ as $x = a{e^{ - \alpha t}} + b{e^{\beta t}}$ , where $a, b, \alpha$ and $\beta $ are positive constants. The velocity of the particle will