Two objects of masses 1 kg and 2 kg are moving with velocities 2m/s and 4m/s respectively. They collide and after the collision, the first object moves at a velocity of 3m/s. What will be the velocity of the second object?

Given, ${\mathrm{m}}_1=1\mathrm{ }\mathrm{kg}$,${\mathrm{m}}_2=2\mathrm{ }\mathrm{kg}$,

Before the collision,

${\mathrm{u}}_1=2\mathrm{ }\mathrm{m}/\mathrm{s}$, ${\mathrm{u}}_2=4\mathrm{ }\mathrm{m}/\mathrm{s}$

After the collision,

${\mathrm{v}}_1=3\mathrm{ }\mathrm{m}/\mathrm{s}$, ${\mathrm{v}}_2=?$

From the law of conservation of momentum, the momentum before the action is equal to the momentum after the action.

${\mathbf{m}}_{\mathbf{1}}{\mathbf{u}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}{\mathbf{u}}_{\mathbf{2}}\mathbf{=}{\mathbf{m}}_{\mathbf{1}}{\mathbf{v}}_{\mathbf{1}}\mathbf{+}{\mathbf{m}}_{\mathbf{2}}{\mathbf{v}}_{\mathbf{2}}$

By substituting the values, we get 

$\Rightarrow 1\times 2+2\times 4=1\times 3+2\times {\mathrm{v}}_2$
$\Rightarrow$$10=3+2{\mathrm{v}}_2$
$\Rightarrow$$2{\mathrm{v}}_2=7$
${\mathbf{\Rightarrow }\mathbf{v}}_{\mathbf{2}}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{m}\mathbf{/}\mathbf{s}$

Hence, the velocity is 3.5 m/s.