Two cars A and B are at positions 100 m and 200 m from the origin at t = 0. They start simultaneously with constant velocities 10 ms^(-1) and 5 ms^(-1)respectively in the same direction. Calculate the time and position at which they will overtake one another.

Two cars A and B are at positions 100 m and 200 m from the origin at t

1.	Two cars A and B are at positions 100 m and 200 m from the origin at t = 0. They start simultaneously with constant velocities 10 ms^(-1) and 5 ms^(-1)respectively in the same direction. Calculate the time and position at which they will overtake one another.
Answer» SOLUTION :`x_(BO) = 200 m , x _(AO)= 100 m, v _(A) = 10 ms ^(-1), 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= (200 - 100) + (5-10) t` `therefore t = (100)/(5)` `therefore t = 20 s` Now, LET both cars overtake each other at distance x from`x_(AO)` `therefore x = c _(AO) + v _(A)t ` `=100 + 10 xx 20` `=100 + 200` `therefore x = 300 m` Note We can also TAKE distance x from `x _(BO) .` For that equation is `x=x _(BO) + v _(B)t.`