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 $\frac{v}{2}$ and downward acceleration $-\frac{a}{2}$
• B. B moves down with initial velocity $\frac{v}{2}$ and downward acceleration $-\frac{a}{2}$
• C. B moves up with initial velocity $\frac{v}{2}$ and upward acceleration $-\frac{a}{2}$
• D. B moves down with initial velocity $\frac{v}{2}$ and upward acceleration $-\frac{a}{2}$

Answer 1

The correct option is A B moves up with initial velocity $\frac{v}{2}$ and downward acceleration $-\frac{a}{2}$

$letinitialco-ordinatesbeA(-d,0),B(0,0),C(d,0)aftertimetAisatpoint(-d,vt)andCisatpoint(d,\frac{1}{2}a{t}^2)linejoiningAandcisy=\frac{\frac{1}{2}a{t}^2-vt}{2d}x+\frac{vt}{2}+\frac{1}{4}a{t}^{2}atx=0,y=\frac{vt}{2}+\frac{1}{4}a{t}^2,whichisdisplacementofB$