A particle is projected vertically upwards from the surface of the earth and returns to the same starting point. Taking the upward direction as positive and the starting point as the origin, which of the following correctly describes the position-time ( y-t ) graph for this motion?

Step-by-step solution

Let the initial velocity be u (upwards, so positive). The acceleration due to gravity is a = -g (downwards). The position y of the particle at any time t is given by the second equation of motion: y = ut - 1 2 gt^2 This is a quadratic equation in t . Since the coefficient of t^2 is negative ( - 1 2 g ), the graph of y versus t is a parabola opening downwards. At t = 0 , y = 0 . The particle reaches a maximum positive height and then returns to y = 0 . Therefore, the graph is a downward-opening parabolic curve start