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

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

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Why distance is taken as negative while finding final momentum?
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The answer is If we see the figure the particle first reaches the top which is at 20 m and then it retards which means that the particle''s speed is getting reduced so here we have not taken the distance to be negative but we have taken the velocity to be negative -(d/t) we have taken this as whole.
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First of all its position which represents displacement and second one displacement is taken negative and not(d/t) as a whole though velocity will be negative in direction but here displacement is taken negative as the particle is returning to its initial position.
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And how could we know that it is retarding.pls explain me this graph.
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but they have asked to find the change in momentum for 4 seconds 

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But why have we taken distance=20 at t=0
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Where is the figures?
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Why we have distance 20m for initial momentum?
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The position at time T craft for a particle of mass 1kg moving along x-axis in shown in figure find impulse on particle at T = 2 4S
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This question has following graph

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This question is the following graph

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What are you looking for?