two fan carts with different fan speeds and different accelerations are started

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.
please give a detailed answer with some explanation

Explanation / Answer

1. just draw the two graph. y=aA*x^2/2. y=xB-aB*x^2/2 2. let y1 = y2 so that aA*t^2/2=xb-aB*t^2/2 so (aA+aB)*t^2/2=xb. so t=sqrt(2xb/(aA+aB))

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