Question

Where x represents the position of the object. The accerlation of the particle at any instant is a=dv/dt?

Answer 1

$\Huge{\underline{\underline{\blue{\mathfrak{Question :}}}}}$

If x represents the position of the object then prove relationship a = dv/dt

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$\Huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

As we know that,

$\LARGE{\boxed{\tt{a \: = \: \frac{v \: - \: u}{t_{2} \: - \: t_{1}}}}}$

Change can be represented as Δ.

$\LARGE \leadsto {\sf{a \: = \: \frac{\Delta v}{\Delta t}}}$

$\LARGE \implies {\sf{\lim_{\Delta t \to 0} }}$

$\LARGE \leadsto {\boxed{\red{\sf{a \: = \: \frac{dv}{dt}}}}}$

∴ Hence relation is verified

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$\Large{\underline{\underline{\sf{Additional \: Information}}}}$

Instantaneous acceleration :- Acceleration of an object in an instant of time is called Instantaneous acceleration.

Units :- m/s²

Definition of acceleration :- Rate of change of velocity .