The speed (v) of a particle moving along a straight line, when it is at a distance (x) from a fixed point on the line, is given by: $$v2$$ $$=$$ $$144$$ $$-9x2$$.Now, match the given columns and select the correct option from the codes given below.

Question

The speed (v) of a particle moving along a straight line, when it is at a distance (x) from a fixed point on the line, is given by: $$v2$$ $$=$$ $$144$$ $$-9x2$$.Now, match the given columns and select the correct option from the codes given below.

Infinity Learn · Accepted Answer

For (i): $$v2$$ $$=$$ $$144-9x2$$  ⇒ $$2vdvdx=0-18x$$⇒a $$=$$ $$-9x$$   ⇒ω$$2$$ $$=9$$ ⇒ω $$=$$ $$3Time$$ period T $$=$$ $$2$$πω $$=$$ $$2$$$$π$$$$3$$ unitsFor (ii): ∵ $$v2$$≥$$0$$ ∴$$144-9x2$$≥$$0$$ ⇒$$x2$$≤$$16$$ ⇒x≤$$4$$⇒Amplitude $$=$$ $$4$$ unitsFor (iii): Maximum velocity $$=$$ Aω $$=$$ (4)(3) $$=$$ $$12$$ unitsFor (iv): At x $$=$$ $$3$$ units, a $$=$$ $$-9x$$ $$=$$ $$-27$$ units

	Column-I		Column-II
i.	Motion is simple harmonic of period	p.	$\frac{2 π}{3} units$
ii.	Maximum displacement from the fixed point is	q.	12 units
iii.	Maximum velocity of the particle	r.	27 units
iv.	Magnitude of acceleration at a distance (S) 3 units from the fixed point is	s.	4 units

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