A point moves with uniform acceleration and ${v_1},\,{v_2}$ and ${v_3}$ denote the average velocities in the three successive intervals of time ${t_1},\,{t_2}$ and ${t_3}$. Which of the following relations is correct
A point moves with uniform acceleration and ${v_1},\,{v_2}$ and ${v_3}$ denote the average velocities in the three successive intervals of time ${t_1},\,{t_2}$ and ${t_3}$. Which of the following relations is correct
$({v_1} - {v_2}):({v_2} - {v_3}) = ({t_1} - {t_2}):({t_2} + {t_3})$
$({v_1} - {v_2}):({v_2} - {v_3}) = ({t_1} + {t_2}):({t_2} + {t_3})$
$({v_1} - {v_2}):({v_2} - {v_3}) = ({t_1} - {t_2}):({t_1} - {t_3})$
$({v_1} - {v_2}):({v_2} - {v_3}) = ({t_1} - {t_2}):({t_2} - {t_3})$
A point moves with uniform acceleration and ${v_1},\,{v_2}$ and ${v_3}$ denote the average velocities in the three successive intervals of time ${t_1},\,{t_2}$ and ${t_3}$. Which of the following relations is correct
Let ${u_1},\,{u_2},\,{u_3}$ and ${u_4}$ be velocities at time $t = 0,\;{t_1},\;({t_1} + {t_2})$ and $({t_1} + {t_2} + {t_3})$respectively and acceleration is a then
${v_1} = \frac{{{u_1} + {u_2}}}{2},\;{v_2} = \frac{{{u_2} + {u_3}}}{2}{\rm{and}}\;{v_3} = \frac{{{u_3} + {u_4}}}{2}$
Also ${u_2} = {u_1} + a{t_1}\;,\;{u_3} = {u_1} + a({t_1} + {t_2})$
and ${u_4} = {u_1} + a({t_1} + {t_2} + {t_3})$
By solving, we get
$\frac{{{v_1} - {v_2}}}{{{v_2} - {v_3}}} = \frac{{({t_1} + {t_2})}}{{({t_2} + {t_3})}}$