Q.A uniform rod AB of mass and length l is at rest on a smooth horizontal surface. An impulse J is applied to the end B, perpebdicular to the rod in the horizontal direction. Speed of particle P at a distance l/6 from the centre towards A of the rod after time t=(pi)ml/12Jpi=22/7

dude this is a very good question but dont expect a reply on an online forum ask a teacher fr a detailed explanation

all i can say is that there r 2 parts in this question

first conserve linear momentum to get centre of mass velocity

then conserve angular momentum as J.R=Iw

write equation about com so that pseudo torque does not have to be applied

from this u will get  ''w'' then at given time vectorially add velocities of com n the velocity of rotation about com to get velocity wrt ground