Explanation:
At time \(t\), velocity of particle is
\({v_t} = 10\;m{s^{ - 1}},\,\,{v_{t + 3}} = 16\;m{s^{ - 1}}\) and \({\mkern 1mu} {\mkern 1mu} {v_{t - 2}} = {v_x}\)
From equation of motion,
\( \Rightarrow v = u + at\)
\( \Rightarrow {v_t} = 0 + at\)
\( \Rightarrow t = \left( {\frac{{10}}{a}} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
\( \Rightarrow {v_{t - 3}} = u + a(t + 3)\)
\( \Rightarrow 16 = 0 + \left( {\frac{{10}}{a} + 3} \right)a = 3a + 10\)
\( \Rightarrow a = 2m{s^{ - 2}}\)
and \(t = 5s\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[{\rm{from Eq}}{\rm{.}}(1)]\)
Now, \({v_{t - 2}} = u + a(t - 2) = 2(t - 2)\)
\( \Rightarrow {v_x} = {v_{t - 2}} = 6m{s^{ - 1}}\)