A car is moving along a straight track with a velocity of $20{\text{ms}}^{-1}$ due East. After 5 s it starts retracing its path with the uniform velocity$\overrightarrow{v}$ . If its average velocity after 15 s is zero, then$\overrightarrow{v}$ is ____       

Given that

A car moving in straight track covered A to B towards east with velocity ${\text{v}}_1=20\text{m/s}$

Time ${\text{t}}_{\text{1}}=5\text{s}$

Displacement $\text{AB}={\text{v}}_{\text{1}}{\text{t}}_{\text{1}}=5\times 20=100\text{m}$

It started retracing back and reached A in $\text{t}=10\text{s}$

With velocity $=\overrightarrow{v}$

So that after t = 15s the total displacement will be zero

i.e. average velocity = 0

BA = 100m $=\text{v}\times 10\text{s}$

$\therefore \overrightarrow{v}=\frac{100}{10}=10\text{m/s}$  towards west.