A gun applies a force F on a bullet which is given by $F = (100 - 0.5 \times 10^{5} t) N$ . The bullet emerges out
with speed 400 m/s. Then, find out the impulse exerted till force on bullet becomes zero. [AIIMS 2019]

Question

A gun applies a force F on a bullet which is given by $F = (100 - 0.5 \times 10^{5} t) N$ . The bullet emerges out
with speed 400 m/s. Then, find out the impulse exerted till force on bullet becomes zero. [AIIMS 2019]

Infinity Learn · Accepted Answer

Force applied by gun,  F $$=$$ $$(100-0.5$$×$$105t)NSpeed$$ of bullet, v $$=$$ $$400$$ $$m/sWhen$$ F $$=$$ $$0$$, then $$100$$ $$-$$ $$0.5$$ X $$105$$ t $$=$$ $$0$$⇒ t $$=$$ $$2$$×$$10-3s$$ Impulse, $$I=$$∫$$Fdt=$$∫$$02$$×$$10-3100-0.5$$×$$105tdt=100t-0.5$$×$$105$$·$$t2202$$×$$10-3=100$$×$$2$$×$$10-3-0.5$$×$$1052$$×$$4$$×$$10-6-0=0.2-0.1=0.1$$ $$N-s$$

A gun applies a force F on a bullet which is given by $F = (100 - 0.5 \times 10^{5} t) N$ . The bullet emerges out
with speed 400 m/s. Then, find out the impulse exerted till force on bullet becomes zero. [AIIMS 2019]

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A gun applies a force F on a bullet which is given by F=100-0.5×105tN. The bullet emerges outwith speed 400 m/s. Then, find out the impulse exerted till force on bullet becomes zero. [AIIMS 2019]

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A gun applies a force F on a bullet which is given by $F = (100 - 0.5 \times 10^{5} t) N$ . The bullet emerges out
with speed 400 m/s. Then, find out the impulse exerted till force on bullet becomes zero. [AIIMS 2019]