Q: A car starts from rest and moves with uniform acceleration ‘a’ At the same instant from the same point a bike crosses with a uniform velocity ‘u’. When and where will they meet ? What is the velocity of car with respect to the bike at the time of meeting ?

Sol: If they meet at the same point then,

S_{c} = S_{b}

$\large \frac{1}{2} a t^2 = u t $

$\large t = \frac{2u}{a}$

Hence , $\large S_b = ut = \frac{2u^2}{a}$

$\large v_c = a t = a \frac{2u}{a} = 2 u$

velocity of car with respect to the bike at the time of meeting

$\large \vec{v_{cb}} = \vec{v_c} – \vec{v_b} $

$\large = 2u-u = u$