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At the initial moment three points A, B ...

At the initial moment three points A, B and C are on a horizontal straight line at equal distances from one another. Point A begins 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

acceleration a/2 and initial velocity v/2 both upwards

B

retardation a/2 and initial velocity v/2 both upwards

C

zero acceleration and initial velocity v

D

acceleration a/2 and initial velocity v both downwards

Text Solution

Verified by Experts

The correct Answer is:
B
Let the three particles be A, B and C located at (0, 0), `(x_(0),0) and (2x_(0),0)` respectively. Initially end A starts moving along positive y axis with constant velocity and C parallel to negative y axis with initial velocity zero but acceleration a.
After time t, coordinates of points A and C respectively are (0, vt) and `(2x_(0),-1//2 at^(2))` Let initial velocity of B is u and acceleration is b towards +ve y-axis.
its coordinates after time t are . As x-coordinates of B is the mid-point of A & C always so y coordinates should also be midpoint as they lie on a straight line.
`rArr u+(bt)/(2)=v/2-(at)/(4)" is identity in t" rArr u=v//2 & b=-a//2`
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