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]

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