# 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

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

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