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.

Explanation

`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.`