Question

The displacement x of a particle moving in one
dimension is related to time by equation t = V(x) + 3
where x is in metre and t is in second. The displacement
when velocity is zero is :
(a) Om (6) 1 m
(c) 9 m (d) 6 m.
$plz \: solve \: it$
​

Answer 1

Correct Question:-

The displacement x of a particle moving in one dimension is related to time by the equation where is in metre and is in second. The displacement when velocity is zero is:

(a) 0 m

(b) 1 m

(c) 9 m

(d) 6 m

Solution:-

The displacement is given by,

$\longrightarrow\sf{t=\sqrt x+3}$

$\longrightarrow\sf{\sqrt x=t-3}$

$\longrightarrow\sf{x=(t-3)^2}$

Velocity of the particle is,

$\longrightarrow\sf{v=\dfrac{dx}{dt}}$

$\longrightarrow\sf{v=\dfrac{d}{dt}\,(t-3)^2}$

$\longrightarrow\sf{v=\dfrac{d[(t-3)^2]}{d(t-3)}\cdot\dfrac{d(t-3)}{dt}}$

$\longrightarrow\sf{v=2(t-3)(1-0)}$

$\longrightarrow\sf{v=2(t-3)}$

$\longrightarrow\sf{t=\dfrac{v}{2}+3}$

Time for which velocity is zero is,

$\longrightarrow\sf{t=\dfrac{0}{2}+3}$

$\longrightarrow\sf{t=3\ s}$

Displacement of the particle at this time is,

$\longrightarrow\sf{x=(3-3)^2}$

$\longrightarrow\underline{\underline{\sf{x=0\ m}}}$

Hence (a) is the answer.