Question

What is instantaneous speed?

Answer 1

Hint: Speed is the ratio of distance travelled and time taken and its magnitude is represented by its unit. Speed describes the motion of a body in one dimension. Any instantaneous value is calculated for a particular moment in time that means when the time interval tends to zero.

Complete answer:
Speed is the distance covered per unit time. Its SI unit is $m{{s}^{-1}}$. It is a scalar quantity. Therefore,
$s=\dfrac{\Delta x}{\Delta t}$ - (1)
Here, $s$ is the speed of a body
$\Delta x$ is the change in position or distance travelled
$\Delta t$ is the time interval
There are different types of speed like instantaneous speed and average speed.
The value of speed calculated at a particular moment in time is called instantaneous speed. In eq (1), when the time interval becomes so small that $\Delta t\approx 0$ then, $\Delta t$ is represented as $dt$ and indicates an infinitesimally small change in time. For the infinitesimally small change in time interval, $dt$ instantaneous speed is calculated.
Therefore, the instantaneous speed is given by-
$s'=\dfrac{dx}{dt}$
For an infinitesimally small time interval, the change in distance is also infinitesimally small but the ratio of distance and time is not zero hence, we calculate instantaneous speed.
Therefore, the speed of a body in a moment in time is called instantaneous speed.

Note:
The average speed is defined as the average distance travelled divided by total time taken. When the instantaneous speed is given as direction, then it becomes instantaneous velocity. Infinitesimally small time interval means very close to zero but not quite zero. Similarly, we can find instantaneous linear velocity, angular velocity, acceleration etc.