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# A particle is dropped from point A at a certain height from ground. It falls freely and passes through three points B,C and D with BC=CD.Time taken for particle to move from B to C is 2 seconds and from C to D is 1 second. Time taken to move from A to B is

$(a)\;0.5 s\quad (b)\;1.5 s \quad (c)\;0.75s \quad (d)\;0.25s$

Let $AB=y$
$BC=CD=h$
$y=\large\frac{1}{2} $$gt^2-----(1) y+h=\large\frac{1}{2}$$g(t+2)^2$-----(2)
$y+2h=\large\frac{1}{2}$$g(t+3)^2$-----(3)
Solving we get $t=0.5 s$