Question

Instantaneous acceleration of a particle is correctly expressed as ______.

Options

• \[\frac{\Delta\vec{v}}{\Delta t}\] for large Δt

• \[\operatorname*{lim}_{\Delta t\to0}\frac{\Delta\vec{v}}{\Delta t}\]

• \[\frac{d\vec{x}}{dt}\]

• \[\frac{d^2\vec{x}}{dt^2}\]

Answer 1

Instantaneous acceleration of a particle is correctly expressed as \[\operatorname*{lim}_{\Delta t\to0}\frac{\Delta\vec{v}}{\Delta t}\].

Explanation:

Instantaneous acceleration is the limiting value of average acceleration when the time interval becomes very small, \[\vec{a}=\lim_{\Delta t\to0}\frac{\Delta\vec{v}}{\Delta t}=\frac{d\vec{v}}{dt}\]​. This gives the acceleration at a particular instant.