Motion Problem - please help?

Question

Two runners A and B initially 200 m apart on a straight track run toward each other. The runner A starts with an initial velocity of 5m/s and maintains a constant acceleration of 0.1 m/s. The runner B starts with an initial velocity of 2 m/s2 and maintains a constant acceleration of 0.3 m/s2. Determine after how long and at what position on the track will they meet. Please help

Answer 1

For constant acceleration, X(T) = X(0) + VoT + 0.5aT²

X := position, Vo := initial velocity, T := time, X(0) := initial position

Put the origin of the coordinate system between the two runners such that X(0) for A is at -100 and X(0) for B is at +100.

We want to solve for when X(T) is the same for both runners.

-100 + 5T + 0.5(0.1)T² = 100 - 2T - 0.5(0.3)T²

T² + 35T - 1000 = 0

T = 18.64 seconds

X = 0.5(0.1)(18.64)² + 5(18.64) - 100 = 10.59 m

Position is at 10.59 m from the origin of the coordinate system which is +110.59 m from where runner A starts and -89.41 m from where runner B starts after 18.64 seconds.