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?

Explanation

To solve the problem step by step, we will analyze the motion of both the car and the bike, determine when and where they meet, and find the velocity of the car with respect to the bike at that moment.

### Step 1: Define the motion of the car
The car starts from rest and moves with uniform acceleration \( a \). The initial velocity \( u_c = 0 \) and the distance covered by the car after time \( t \) can be calculated using the equation of motion:
\[ s_c = u_c t + \frac{1}{2} a t^2 \]
Since \( u_c = 0 \), this simplifies to:
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