Question

please answer the question:)​

Answer 1

$\mathcal{\green{\underbrace{\orange{SOLUTION:-}}}}$

GIVEN :-

✍️ Velocity of a particle as a function of time t is,

• v = 2t m/s

TO FIND :-

• The position of the particle at “t = 1s”

CALCULATION :-

✍️ we have know that,

• v = ds/dt

Where,

• v = Velocity

• ds = change in position

• dt = change in time

$\rm{\implies\:ds\:=\:v.dt\:}$

✍️ According to the question, particle is at origin initially [$\therefore\:\rm{t\:=\:0\:s}$ ] . So, let after 1 second the position of the particle is at ‘s ’ .

$\rm{\implies\:\int\limits^s_0\:ds\:=\:\int\limits^1_0\:v\:.\:dt\:}$

$\rm{\implies\:s\:=\:\int\limits^1_0\:{2t\:.\:dt}\:}$

$\rm{\implies\:s\:=\:\left[\dfrac{2t^2}{2}\right]_0^1\:}$

$\rm{\implies\:s\:=\:\left[t^2\right]_0^1\:}$

$\rm{\implies\:s\:=\:1^2\:-\:0^2\:}$

✍️ So, at “t = 1 s”

$\rm{\purple{\implies\:s\:=\:1\:m}}$

$\therefore\:\rm{\blue{Position\:of\:the\:particle\:at\:1s\:is\:\:\underline\bold{1\:meter}\:}}$