A small block of $$mass1$$ kg starts moving with constant velocity $$2$$ $$m/s$$ on a smooth long plank of mass $$10$$ kg which is also pulled by a horizontal force F $$=$$ $$10$$ t where t is in seconds and F in Newton's (the$$ initial velocity of the plank is $$zero)Displacement$$ of $$1$$ kg block with respect to plank at the instant when both have same velocity isThe time $$(t$$≠$$0) at which displacement of block and plank with respect to ground is same will beRelative velocity of plank with respect to block when acceleration of plank is $$4$$ $$m/s2$$ will be

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Infinity Learn · Accepted Answer

Acceleration of $$10$$ kg plank,                       $$a=Fm=10t10=t$$∴   $$dv=adtor$$   ∫$$0v$$ $$dv=$$∫$$0t$$ tdtor   $$v=t22or$$    $$t=2s$$ when $$v=2m/s$$       $$s1=vt=2$$×$$2=4m$$           $$=$$ displacement of $$1kg$$       $$s2=$$∫$$0t$$ $$vdt=$$∫$$0t$$ $$t22dt=t36At$$  $$t=2s$$                      $$s2=(2)36=43m$$   ∴              $$s12=s1$$−$$s2=4$$−$$43=83ms1=s2$$  or  $$2t=t36$$∴ $$t=23sa=t$$∴ $$a=4ms2$$ at $$t=4s$$         $$vPB=vP$$−vB        $$=t22$$−$$2$$        $$=6m/s$$     (at$$ $$=$$ $$4s)

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