A particle moves with constant acceleration, | vedclass

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Question

Let $u_{1}, u_{2}, u_{3}$ and $u_{4}$ be the velocities at times $t=0, t_{1},\left(t_{1}+t_{2}\right)$ and $\left(t_{1}+t_{2}+t_{3}\right)$ respective

Vedclass · Accepted Answer

$\frac{{{v_1}\, - \,{v_2}}}{{{v_2}\, - \,{v_3}}}\, = \,\frac{{{t_1}\, + {t_2}}}{{{t_2}\, + \,{t_3}}}$

Vedclass · Answer

Let $u_{1}, u_{2}, u_{3}$ and $u_{4}$ be the velocities at times $t=0, t_{1},\left(t_{1}+t_{2}\right)$ and $\left(t_{1}+t_{2}+t_{3}\right)$ respectively. Let $'a'$ be the acceleration.

Now, $\quad \mathrm{v}_{1}=\frac{\mathrm{u}_{1}+\mathrm{u}_{2}}{2}, \quad \mathrm{v}_{2}=\frac{\mathrm{u}_{2}+\mathrm{u}_{2}}{2}$ and $\mathrm{v}_{3}=\frac{\mathrm{u}_{2}+\mathrm{u}_{4}}{2}$

Also $\quad \mathrm{u}_{2}=\mathrm{u}_{1}+\mathrm{at}_{1}, \mathrm{u}_{3}=\mathrm{u}_{1}+\mathrm{a}\left(\mathrm{t}_{1}+\mathrm{t}_{2}\right)$ and $\quad \mathrm{u}_{4}=\mathrm{u}_{1}+\mathrm{a}\left(\mathrm{t}_{1}+\mathrm{t}_{2}+\mathrm{t}_{3}\right)$

By solving, we get $\frac{v_{1}-v_{z}}{v_{2}-v_{2}}=\frac{\left(t_{1}+t_{2}\right)}{\left(t_{2}+t_{2}\right)}$

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

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