Question

A particle starts from the origin of co-ordinates at time t = 0 and moves in the xy plane with a constant acceleration  in the y-direction. Its equation of motion is y = x 2. Its velocity component in the x-direction is

Answer 1

Bravo! for Questioning.. Its an IIT Question!

Answer:

Velocity Component) y-direction= √g/2β

Explanation:

Since, displacement along x-axis has;

                 S = ut + 1/2gt²

                 x = ut   ( since a=g=0 in x-axis )

                 t = x/u   ______ (1)

Since, displacement along y-axis has;

                 S = ut + 1/2gt²

                 y = 1/2 gt²  ( since u= 0 in y-axis )

Now,

                 y = 1/2 g( x/u)²  ( from (1) )

                 y = 1/2 g × x²/u²

             βx² = 1/2 g × x²/u²   ( Given; y = βx² )

               β = 1/2 g × u²

              2β = 1/g u²

          g/ 2β = u²

                u = √g/2β

Hence, Its velocity component in the x-direction is u = √g/2β.

Hope it helps ;-))