Two cars A and B are at positions 50 m and 100 m from the origin at t = 0. They start simultaneously with constant velocities 10 m/s and 5 m/s respectively in the same direction. Find the time at which they will overtake one another.

Two cars A and B are at positions 50 m and 100 m from the origin at t

1.	Two cars A and B are at positions 50 m and 100 m from the origin at t = 0. They start simultaneously with constant velocities 10 m/s and 5 m/s respectively in the same direction. Find the time at which they will overtake one another.
Answer» 10 s 20 s 5 s 15 s Solution :Position of both cars `x _(A0) =50 m and x_(B0) = 100 m` respectively at `t=0` from the origin. Here, `V _(A) = 10 ms ^(-1) and V_(B) = 5 ms ^(-1)` Now, `x_(B) - x_(A) = (x_(BO) -x _(AO)) + (V_(B) - V_(A))t ` Suppose, at `t=t,` both cars OVERTAKE each other. `THEREFORE x_(B) =x_(A) and x_(B) -x_(A) =0` `therefore 0= (100 -50) + (5-10) t` `therefore t = (50)/(5) = 10 s `