If `v_x` and `v_y` are the components of instantaneous velocity, then represent the velocity vectorially. Express the magnitude and direction of velocity.

Explanation

We know that `vecv=Lt_(/_\t to0)(/_\vecr)/(/_\t)=(dvecr)/(dt)`
Since `/_\vecr=(x_1-x_2)hati+(y_1-y_2)hatj`
`Lt_(/_\t to0)(/_\vecr)/(/_\t)=hatiLt_(/_\t to0)((/_\x)/(/_\t)+hatjLt_(/_\t to0)((/_\y)/(/_\t)`
i.e, `vecv=(dvecr)/(dt)=hati(dx)/(dt)+hatj(dy)/(dt)=v_xhati+v_yhatj`
`|vecv|=sqrt(v_x^2+v_y^2)` gives the magnitude of `vecv` and
`prop=tan^(-1)((v_y)/(v_x))` where `'prop'` is the direction of 'v' w.r.t x-axis.