Question

Position of a particle moving along a straight line is given by x=2t^(2)+t .The velocity at t=2sec in m/s will be​

Answer 1

Explanation:

in this way we can solve the given problem my friend please check your answer

Answer 2

Given :

▪ Equation of position of a particle moving along a straight line has been provided.

$\bigstar\:\underline{\boxed{\bf{\gray{x=2t^2+t}}}}$

To Find :

▪ Velocity of the particle at t = 2s.

Formula :

→ Formula of Instantaneous velocity is given by

$\bigstar\:\underline{\boxed{\bf{\green{v=lim(\Delta t\to 0)\:\dfrac{\Delta x}{\Delta t}=\dfrac{dx}{dt}}}}}$

Calculation :

$\dashrightarrow\sf\:v=\dfrac{dx}{dt}\\ \\ \dashrightarrow\sf\:v=\dfrac{d(2t^2+t)}{dt}\\ \\ \dashrightarrow\sf\:v=4t+1\\ \\ \rm\red{\dag\:putting\:t=2,\:we\:get}\\ \\ \dashrightarrow\sf\:v=4(2)+1\\ \\ \dashrightarrow\sf\:v=8+1\\ \\ \dashrightarrow\underline{\boxed{\bf{\purple{v=9\:mps}}}}\:\orange{\bigstar}$

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$\star\sf\:y=x^n\\ \\ \star\sf\:\dfrac{dy}{dx}=nx^{n-1}$