The relation between time ‘t’ and distance x for a moving particle is $$t=$$α$$x2+$$βx where α and β are constants, If v is the velocity at distance x, then the retardation of the particle is

Question

The relation between time ‘t’ and distance x for a moving particle is $$t=$$α$$x2+$$βx where α and β are constants, If v is the velocity at distance x, then the retardation of the particle is

Infinity Learn · Accepted Answer

given relation time is $$t=$$α$$x2+$$βx differentiate w.r.t. displacement x $$dtdx=2$$α$$x+$$β$$velocity=v=dxdt=12$$α$$x+$$β$$---(1)$$∴$$v=2$$α$$x+$$β−$$1differentiate$$ w.r.t. x $$dvdx=$$−$$12$$α$$x+$$β−$$2(2$$α$$)substitute$$ equation $$(1)dvdx=$$−$$2$$α$$2$$α$$x+$$β$$2=$$−$$2$$α$$v2$$  we know,$$a=v$$.dvdx         since $$a=dvdt=dvdtdxdx=dxdtdvdx=vdvdx$$ $$a=$$−$$2$$α$$v3$$ retardation of the $$paticle=2$$α$$v3$$

The relation between time ‘t’ and distance x for a moving particle is $t = α x^{2} + β x$ where $α$ and $β$ are constants, If v is the velocity at distance x, then the retardation of the particle is

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The relation between time ‘t’ and distance x for a moving particle is t=αx2+βx where α and β are constants, If v is the velocity at distance x, then the retardation of the particle is

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The relation between time ‘t’ and distance x for a moving particle is $t = α x^{2} + β x$ where $α$ and $β$ are constants, If v is the velocity at distance x, then the retardation of the particle is