Question

the position time graph for a particle of mass 1 kg moving along x-axis is shown in figure.Find impulse on particle at t= 4s.

Answer 1

impulse = change in momentum
e.g., $I=P_f-P_i$

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, $P_f=mv_f$
$P_f=1kg\times-5m/s=-5kgm/s$....(i)

and $P_i=mv_i$
$P_i=1kg\times5m/s=5kgm/s$....(ii)


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

Answer 2

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