Q: A particle of mass 2 kg is initially at rest. A force acts on it whose magnitude changes with time. The force time graph is shown below .The velocity of the particle after 10 s is
(a) 20 ms-1
(b) 10 ms-1
(c) 75 ms-1
(d) 50 ms-1
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Ans: (d)
Sol: Area of F-t graph gives change in Linear momentum .
change in momentum , ΔP = m v – m u
Since , u = 0 ;
ΔP = m v ….(i)
Area of F-t graph is
$\displaystyle A = \frac{1}{2}\times 2 \times 10 + 2 \times 10 + \frac{1}{2}(10+20)2 + \frac{1}{2} \times 4 \times 20 $
A = 100 ….(ii)
From (i) & (ii)
m v = 100
2 v = 100
v = 50 m/s