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.

Options

A. 10 s
B. 20 s
C. 5 s
D. 15 s

Answer

A

Explanation

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 `