Question

The force F acting on a particle of mass 1 kg is indicated by the force-time graph as shown. If the partial starts from rest, then the speed of the particle at the end of 6 s will be

• A. 3 m $s^{-1}$
• B. 12 m $s^{-1}$
• C. 9 m $s^{-1}$
• D. 18 m $s^{-1}$

Answer 1

The correct option is B 12 m $s^{-1}$

Area under $f-t$ graph gives change in momentum

for $0$ to $2s$

$△P_1=\frac{1}{2}\times 2\times 6=+6kgm/s$

for $2$ to $4sec$

$△P_2=2\times (-3)=-6kg-m/s$

for $4$ to $8sec$

$△P_3=\left(4\right)\times 3=12kg-m/s$

So total change in momentum $0$ to $8sec$

$△P_{net}=△P_1+△P_2+△P_3$

$=+6-6+12$

$=12kg-m/s$

$△P_{net}=12N$