An object of mass $$4$$ kg is moving along $$x-axis$$ such that its position $$x-$$ varies with time ‘t’ as $$x2$$ $$=$$ $$16t3$$, with x in metre and t in $$sec$$. Work done as a function of time can be shown as

Question

An object of mass $$4$$ kg is moving along $$x-axis$$  such that its position   $$x-$$ varies with time ‘t’ as  $$x2$$ $$=$$ $$16t3$$,  with x in metre and t in $$sec$$.   Work done as a function of time can be shown as

Infinity Learn · Accepted Answer

given position x varying with time t $$x2$$ $$=$$ $$16t3$$ take square root both sides                        x $$=$$  $$4t32$$                                                                            differentiate x with respect to time t dxdt   $$=$$   $$4$$×$$32$$ $$t1/2$$ dxdt   $$=$$ $$6$$ $$t1/2---(1)$$ $$dx=6$$ $$t1/2dt---(2)$$ again differentiate $$eqn(1)$$ with respect to time t                                                         ⇒$$d2xdt2$$   $$=$$   $$3t$$ $$=acceleration---(3)$$ work done $$dW=F$$.dx here force $$F=ma$$ ⇒$$dW=ma$$ .dx substitute equations (2),(3) and $$m=4kg$$ in the above equation ⇒$$dW=43t6$$ $$t1/2dt$$ ⇒$$dW=72$$ dt integrating ∫$$dW=$$∫$$72$$ dt ⇒$$W=72$$ t ⇒Work α time

An object of mass 4 kg is moving along x-axis such that its position x- varies with time ‘t’ as $x^{2} = 16 t^{3}$ , with x in metre and t in sec. Work done as a function of time can be shown as

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An object of mass 4 kg is moving along x-axis such that its position x- varies with time ‘t’ as x2 = 16t3, with x in metre and t in sec. Work done as a function of time can be shown as

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An object of mass 4 kg is moving along x-axis such that its position x- varies with time ‘t’ as $x^{2} = 16 t^{3}$ , with x in metre and t in sec. Work done as a function of time can be shown as