Question

The displacement of car moving in x-axis is given by x = 18t + t2. Calculate,

instantaneous velocity at t = 2 sec.​

Answer 1

Given :

The displacement of car moving in x-axis is given by, x = 18t + t²

To Find :

Instantaneous velocity of car at t = 2s.

Solution :

★ In order to find Instantaneous velocity of particle, we need to differentiate the given displacement equation with respect to time.

Instantaneous velocity :

$\dag\:\underline{\boxed{\bf{\red{v=\lim\limits_{t\to0}\:\dfrac{\Delta x}{\Delta t}=\dfrac{dx}{dt}}}}}$

$\sf:\implies\:v=\dfrac{dx}{dt}$

$\sf:\implies\:v=\dfrac{d(18t+t^2)}{dt}$

$\sf:\implies\:v=\dfrac{d(18t)}{dt}+\dfrac{d(t^2)}{dt}$

$\sf:\implies\:v=18+2t$

Putting t = 2, we get

$\sf:\implies\:v=18+2(2)$

$\sf:\implies\:v=18+4$

$:\implies\:\underline{\boxed{\bf{\gray{v=22\:ms^{-1}}}}}$

Answer 2

Given :

The displacement of car moving in x-axis is given by, x = 18t + t²

To Find :

Instantaneous velocity of car at t = 2s.

Solution :

★ In order to find Instantaneous velocity of particle, we need to differentiate the given displacement equation with respect to time.

Instantaneous velocity :

$\dag\:\underline{\boxed{\bf{\red{v=\lim\limits_{t\to0}\:\dfrac{\Delta x}{\Delta t}=\dfrac{dx}{dt}}}}}$

$\sf:\implies\:v=\dfrac{dx}{dt}$

$\sf:\implies\:v=\dfrac{d(18t+t^2)}{dt}$

$\sf:\implies\:v=\dfrac{d(18t)}{dt}+\dfrac{d(t^2)}{dt}$

$\sf:\implies\:v=18+2t$

Putting t = 2, we get

$\sf:\implies\:v=18+2(2)$

$\sf:\implies\:v=18+4$

$:\implies\:\underline{\boxed{\bf{\gray{v=22\:ms^{-1}}}}}$