Question

Two fan carts with different fan speeds and different accelerations are started from rest some
distance from one another.
Cart A begins at position 0 with a velocity of zero and an acceleration of aA to the right.
Cart B begins at position xB with a velocity of zero and an acceleration of aB to the left.
1. Draw a qualitative position-time graph to represent the situation.
2. Develop an algebraic expression in terms of the variables below that will predict exactly where the carts will meet, indicated by xf.

Answer 1

Xa = 0 + 0 t + .5 A t^2
Xb = XB + 0t - .5 B t^2

they will hit when Xa = Xb

.5 A t^2 = XB - .5 B t^2

.5 t^2 ( A+B ) = XB

t^2 = 2 XB/(A+B)
so
Xa = Xb = .5 A t^2 = A XB /(A+B)

Answer 2

That is the answer?