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Question

# At the initial moment three points A, B and C are on a horizontal straight line at equal distances from one another. Point A beings to move vertically upward with a constant velocity v and point C vertically downward without any initial velocity but with a constant acceleration a. How should point B move vertically for all the three points to be constantly on one straight line. The points begin to move simultaneously.

A
B moves up with initial velocity v2 and downward acceleration a2
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B
B moves down with initial velocity v2 and downward acceleration a2
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C
B moves up with initial velocity v2 and upward acceleration a2
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D
B moves down with initial velocity v2 and upward acceleration a2
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Solution

## The correct option is A B moves up with initial velocity v2 and downward acceleration −a2letinitialco−ordinatesbeA(−d,0),B(0,0),C(d,0)aftertimetAisatpoint(−d,vt)andCisatpoint(d,12at2)linejoiningAandcisy=12at2−vt2dx+vt2+14at2atx=0,y=vt2+14at2,whichisdisplacementofB

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