Question

Write short notes on instantaneous speed and instantaneous velocity. Give examples.

Answer 1

Instantaneous speed:

1. The rate of change of distance with respect to a very short time interval (which is almost equal to zero) is called instantaneous speed.
2. It is a scalar quantity i.e. it is independent of the direction of motion.
3. Instantaneous speed$=\underset{t\to T}{\lim }\frac{dx}{dt}$. Here, $x$ is the distance.
4. Its unit is $m{s}^{-1}$.
5. For example, the speed of the particle moving on a straight path, $x=2t+4$ at time $5s$ will be an instantaneous speed.

Instantaneous velocity:

1. Instantaneous velocity is defined as the rate of change of position for a small interval of time (almost equal to zero).
2. It is a vector quantity i.e. it has both magnitude and direction.
3. Instantaneous velocity = $=\underset{t\to T}{\lim }\frac{dx}{dt}$ where $dx$ is the change in position and $dt$ is the time interval.
4. Its unit is also $m{s}^{-1}$.
5. The magnitude of instantaneous velocity is equal to instantaneous speed.
6. For example, the velocity of the particle moving on a curved path, $x=5t^2+5$ at time $5s$ will be an instantaneous velocity.