A pebble is released from rest from a bridge and falls freely into a river below. Taking the point of release as the origin ( y = 0 ) and the downward direction as positive, which of the following graphs correctly represents the variation of the pebble's displacement ( y ) with time ( t ) before it hits the water? [Refer to the given graphs]

Step-by-step solution

The pebble is released from rest, so its initial velocity is u = 0 . The point of release is taken as the origin ( y = 0 ) and the downward direction is taken as positive. Therefore, the acceleration of the pebble is a = +g . Using the second equation of motion, the displacement y at any time t is given by: y = ut + 1 2 at^2 Substituting u = 0 and a = g , we get: y = 1 2 gt^2 This equation represents a parabola opening upwards, passing through the origin. As time t increases, the displacement y increases quadratica