Question

A particle of mass 2 kg is initially at rest. A fore acts on it whose magnitude changes with time. The force - time graph is shown below. The velocity of the particle after 10s is

Answer 1

see, first we should understand, what is the area of force-time graphs shows. It's the impulse. And impulse is equals to change in momentum.
first find impulse,
impluse = area
             =((1/2)×2×10)+ (2×10)+ ((1/2)×(10+20)×2)+((1/2)×4×20)
             =10+20+30+40
             =100 N-s
now, impulse = change in momentum
                      =m×v - m×u
where v= final velocity and u =initial velocity =0
so, 100 = 2×v 
⇒v = 50 m/s
hope this will help you 

Answer 2

see the attached document please....

7f51c33675d86c9daf22c60ceab8a72e.docx