Question

x=t-1/t find v and a by defferentiation​

Answer 1

Answer -

Here, we are given distance in terms of time -

$\implies$$\sf x = t - \frac{1}{t}$

$\implies$$\sf x = t - t^{-1}$

We know that,

$\sf v = \frac{dx}{dt}$

Differentiating with respect to time :-

$\implies$$\sf v = \frac{d(t - t^{-1})}{dt}$

$\implies$$\sf v = t^{0-1} - t^{-1-1}$

$\implies$$\sf v = t^{-1} - t^{-2}$

$\implies$$\boxed{\sf v = \frac{1}{t} -\frac{1}{t^2}}$

We also know that,

$\sf a = \frac{dv}{dt}$

Differentiating with respect to time :-

$\implies$$\sf a = \frac{d(t^{-1} - t^{-2})}{dt }$

$\implies$$\sf a = t^{-1-1} - t^{-2-1}$

$\implies$$\sf a = t^{-2} - t^{-3}$

$\implies$$\boxed{\sf a = \frac{1}{t^2} -\frac{1}{t^3}}$