Question

the position (x) time(t) graph for a particle of mass 1 kg moving along x axis .find impulse on particle at t=4sec

answer is 10kgm/s

Answer 1

 I am answering this based on that diagram
Impulse = Pf - Pi        
 (where P = momentum = mv)
Pi = m(d/t) = 1(20/4) = 5 kg m/s
Pf = m(d/t) = 1(-20/4) = -5 kg m/s
I = Pf - Pi = -5 -5 = -10 kg m/s
i hope it will help youregards

Answer 2

impulse = change in momentum

e.g.,

here in graph it is clear that , velocity of particle from 0 to 4 sec is positive { 20/4 = 5m/s} and velocity of particular from 4 to 8 sec is negative { -20/4 = -5 m/s}.

so,

....(i)

and

....(ii)

Impulse = -5 - 5 = -10 kgm/s [from eqs. (i), (ii)]