Question

the position of a particles moving along a straight line is given by X=2-5t+t^3. find the equation of velocity.

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Answer 1

Answer :

The position of a particle moving along a straight line is given by

• x = 2 - 5t + t³

We have to find equation of velocity.

$\star$ Instantaneous velocity of moving is given by

$\displaystyle\dag\:\boxed{\bf{\pink{v=\lim_{\Delta t\to 0}\:\dfrac{\Delta x}{\Delta t}=\dfrac{dx}{dt}}}}$

∴ In order to find equation of velocity, we have to differentiate the given equation of position with respect to time.

➝ v = dx/dt

➝ v = d(2 - 5t + t³)/dt

➝ v = -5 + 3t²

★ Remember :

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

$\star\sf\:y=0\:\longrightarrow\:\dfrac{dy}{dx}=0$

$\star\sf\:y=x\:\longrightarrow\:\dfrac{dy}{dx}=1$