Question

Which of the following represents the instantaneous velocity?

• A. ${lim}_{\Delta t\to 0}\frac{\Delta \overrightarrow{S}}{\Delta t}$
  
• B. $\frac{\Delta \overrightarrow{S}}{\Delta t}$
• C. $\frac{S}{\Delta t}$
• D. None of the above

Answer 1

The correct option is A ${lim}_{\Delta t\to 0}\frac{\Delta \overrightarrow{S}}{\Delta t}$


Instantaneous velocity is a vector quantity. It is defined at an instant of time.
Hence reducing the time interval to infinitesimal small i.e taking the limit of $\Delta t\to 0$, while defining $\frac{\Delta \overrightarrow{S}}{\Delta t}$ will yield the instantaneous velocity.
$\Rightarrow {lim}_{\Delta t\to 0}\frac{\Delta \overrightarrow{S}}{\Delta t}=\frac{d\overrightarrow{S}}{dt}$
Here, $v_{\text{instantaneous}}=\frac{d\overrightarrow{S}}{dt}$
$\therefore$Option $\left(a\right)$ is correct.