Question

The equation of motion of a particle is s=t^3+t^2+t where s is in meters and t in second find the velocity when t=2

Answer 1

Given :

▪ The equation of motion of a particle has been provided.

$\bigstar\:\underline{\boxed{\bf{\red{s=t^3+t^2+t}}}}$

• s is in meter
• t is in second

To Find :

▪ Instantaneous velocity of particle at t = 2s

Concept :

☞ Formula of instantaneous velocity is given by

$\bigstar\underline{\boxed{\bf{\purple{v=lim(\Delta t \to 0)\:\dfrac{\Delta s}{\Delta t}=\dfrac{ds}{dt}}}}}$

Calculation :

$\Rightarrow\sf\:v=\dfrac{ds}{dt}\\ \\ \Rightarrow\sf\:v=\dfrac{d(t^3+t^2+t)}{dt}\\ \\ \Rightarrow\sf\:v=3t^2+2t+1\\ \\ \rm\red{\dag\:putting\:t=2,\:we\:get}\\ \\ \Rightarrow\sf\:v=3(2)^2+2(2)+1\\ \\ \Rightarrow\sf\:v=3(4)+4+1\\ \\ \Rightarrow\underline{\boxed{\bf{\gray{v=17\:mps}}}}$

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