If the distance covered by a particle is pivenby relation x= at^2 The

1.	If the distance covered by a particle is pivenby relation x= at^2 The particle is moving with(where a is constant) :(1) constant acceleration2) zero acceleration(3) variable acceleration(4) none of these please answer reliable with reason......
Answer» Answer Acceleration is constant GIVEN Position of the particle is given by : $\tt \: x = a {t}^{2}$ To finD Type of acceleration the particle is executing DIFFERENTIATING x w.r.t to t,we GET velocity of the particle : $\sf \: v = \dfrac{dx}{dt} \\ \\ \leadsto \: \sf \: v = \dfrac{d(a {t}^{2} )}{dt} \\ \\ \leadsto \: \sf \: v = a \times \dfrac{d( {t}^{2} )}{dt} \\ \\ \leadsto \: \boxed{ \boxed{ \sf \: v = 2at \: {ms}^{ - 1}}}$ Differentiating v w.r.t to t,we get acceleration of the particle : $\sf \: a = \dfrac{dv}{dt} \\ \\ \leadsto \: \sf \: a = \dfrac{d(2at)}{dt} \\ \\ \leadsto \: \: \boxed{ \boxed{ \sf \: a \: = 2a \: {ms}^{ - 2} }}$ SINCE, $\huge{ \boxed{ \boxed{ \sf \: a \: \propto \: {t}^{0} }}}$ Acceleration is independent of TIME here and shows no remarkable change Option (A) is correct

If the distance covered by a particle is pivenby relation x= at^2 The particle is moving with(where a is constant) :(1) constant acceleration2) zero acceleration(3) variable acceleration(4) none of these please answer reliable with reason......

Answer»

Answer

Acceleration is constant

GIVEN

Position of the particle is given by :

$\tt \: x = a {t}^{2}$

To finD

Type of acceleration the particle is executing

DIFFERENTIATING x w.r.t to t,we GET velocity of the particle :

$\sf \: v = \dfrac{dx}{dt} \\ \\ \leadsto \: \sf \: v = \dfrac{d(a {t}^{2} )}{dt} \\ \\ \leadsto \: \sf \: v = a \times \dfrac{d( {t}^{2} )}{dt} \\ \\ \leadsto \: \boxed{ \boxed{ \sf \: v = 2at \: {ms}^{ - 1}}}$

Differentiating v w.r.t to t,we get acceleration of the particle :

$\sf \: a = \dfrac{dv}{dt} \\ \\ \leadsto \: \sf \: a = \dfrac{d(2at)}{dt} \\ \\ \leadsto \: \: \boxed{ \boxed{ \sf \: a \: = 2a \: {ms}^{ - 2} }}$

SINCE,

$\huge{ \boxed{ \boxed{ \sf \: a \: \propto \: {t}^{0} }}}$

Acceleration is independent of TIME here and shows no remarkable change