The term instantaneous velocity refers to the rate of change of an object's position over an extremely short (almost zero) time interval. It's measured in m/s, the standard SI unit. On the other hand, instantaneous speed is simply the absolute value of the instantaneous velocity. It possesses the same value as the instantaneous velocity but lacks direction.
Simply put, the instantaneous velocity refers to the velocity of an object at a specific moment in time. It's defined as the velocity of a moving object at a particular instant.
For an object moving with uniform velocity, its instantaneous velocity is identical to its average velocity.
Instantaneous velocity is calculated in a manner similar to average velocity, but the time interval considered is much smaller. As this time interval approaches zero, the displacement also tends to zero. However, the ratio of displacement to time is non-zero and is termed as instantaneous velocity.
Instantaneous Velocity Formula
The formula for instantaneous velocity is given as follows:
Where,
Δt is a small time interval.
V i represents the instantaneous velocity.
s stands for displacement.
t denotes time.
Unit of Instantaneous Velocity
The SI unit of instantaneous velocity is m/s. It is a vector quantity. It can also be determined by the slope of the distance-time graph or x-t graph.
Instantaneous Velocity Example
Consider an object whose displacement varies with time as (8t 2 + 3t + 5) m. We can calculate the instantaneous velocity at any given time as follows:
s = (8t 2 + 3t + 5)
Velocity (v) =
=
= 16t + 3
To find the instantaneous velocity at t = 4 sec, we substitute t = 4 into the velocity expression.
Instantaneous velocity at t = 4 sec = (16×4 + 3) = 67 m/s
Now, let's calculate the average velocity for 4 seconds.
The average speed for a given time interval is the total distance divided by the total time. As this time interval approaches zero, the distance travelled also approaches zero. However, the ratio of distance to time is non-zero and is termed as the instantaneous speed. In simpler terms, the instantaneous speed at any given time is the magnitude of the instantaneous velocity at that time.