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  4. Velocity v of a particle moving along x axis as a function of time is given by v = 2t m/s. Initially the particle is to the right of the origin and 2 m away from it. Find the position (distance from origin) of the particle after first 3 s

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Q. Velocity $v$ of a particle moving along x axis as a function of time is given by $v = 2t\, m/s$. Initially the particle is to the right of the origin and $2 \,m$ away from it. Find the position (distance from origin) of the particle after first $3\,s$Physics Question Image

Motion in a Straight Line

Solution:

$ v = 2t$
$\int\limits_z^x dx = \int\limits_0^3 v\,dt$
$\Rightarrow x - 2 = \int\limits_0^3 2t\,dt$
$\Rightarrow x - 2 = \left[\frac{2t^{2}}{2}\right]_{0}^{3}$
$\Rightarrow x = 11\,m$