A particle is moving unidirectional on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) – time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale):

Step-by-step solution

Here Power is constant, Hence, P = F v = m a v = a v = c o n s t a n t . a v = k v d v d x × v = k ∫ 0 v v 2 d v = k ∫ 0 x d x ∴ v = 3 k 1 / 3 × x 1 / 3 ⇒ v = A x 1 / 3 w h e r e A = 3 k 1 / 3 = c o n s t a n t . . . . 1 Also, v = d x d t ∴ d x d t = A x 1 / 3 ⇒ ∫ 0 d d x x 1 / 3 = A ∫ 0 t d t Simplifying further we get, ⇒ d = A t 3 / 2 . . . 2 From equations 1 & 2 its clear that the graph won't be straight line so first & third options cant be correct. Now, from equation 1 its clear that when x is increased then t