Question

The distance x of a particle moving in one dimension, under the action of a constant force is related to time by equationt=x+3, where x is in metre and t is in seconds. Find the displacement of the particle when its velocity is zero.​

Answer 1

Question :-

The distance x of a particle moving in one dimension, under the action of a constant force is related to time by equationt=x+3, where x is in metre and t is in seconds. Find the displacement of the particle when its velocity is zero

Answer :-

Given :-

• Equation : t = x + 3

Solution :-

$\small{ \sf{ \: \: \: \: ⇒ \: t = √x+3}} \\ \small{ \sf{⇒ √x = t−3 }}\\ \small { \sf{\: \: \: \: \: \: \: \: ⇒ \: </p><p> x=t^2 −6t+9 }}$

$\small{ \sf{dt/dx \: is \: the \: velocity}}$

$\small{ \sf{⇒ dt/dx =2t−6 }}\\ \small{ \sf{</p><p> v=0}}</p><p>$

$\small{ \sf{ 2t−6=0 }}\\ \small{ \sf{</p><p> \: which \: will \: give \: us \: 3 \: so \: t=3</p><p> \: at \: t=3 }}\\ \small{ \sf{</p><p>⇒x=3−3y }}\\ \small{ \sf{</p><p>so, \: there \: will \: be \: 0 \: displacement.}} \\ \small{ \sf{</p><p>Hence, \: the \: answer \: is \: 0.}}</p><p>$