How to Find Instantaneous Velocity
The instantaneous velocity of an object is the velocity at a definite instant of time. Velocity is the alteration in position apportioned by the change in time. While the instantaneous velocity implies the limit of velocity as the change in time approaches zero (0). This is equal to the derivative of position in regards to time. Instantaneous velocity is a vector, and thus it consists of a magnitude (a value) and a direction. The SI unit used to measure instantaneous velocity is meters per second (m/s).
Hence, instantaneous velocity formula is as below:
Instantaneous velocity = limit as change in time goes to zero (change in position/change in time) = derivative of position with respect to time
Where,
v\[^{\rightarrow lim}\] \[_{\Delta \rightarrow 0}\] (Δr\[^{\rightarrow}\] / Δt) = (dr\[^{\rightarrow}\]/dt)
v\[^{\rightarrow}\] = instantaneous velocity (m/s)
Δr\[^{\rightarrow}\] = vector change in position (m)
Δt = change in time (s)
dr\[^{\rightarrow}\]/dt = derivative of vector position with respect to time (m/s)
Why to Calculate Velocity?
Velocity is a measure of how rapidly an object travels from one position to another. If an object is accelerating or decelerating, the velocity of that particular object modifies with time and it could be found out using the instantaneous velocity formula.
In the motion of any particle generally, we are required to measure its velocity and speed in a given time period. However, sometimes we are more inclined to find the value of the velocity at a certain point of time for a very short period of time. Instantaneous velocity is that kind of velocity of a particle in motion. This can be identified as the average velocity, but we may narrow down the time period so that it reaches zero. If a moving object consists of a standard velocity over a time period, its average and instantaneous velocities may be the same.
Solved Examples
Let's learn how to find instantaneous velocity. Below are a few instantaneous velocity examples for a better understanding of the instantaneous velocity concept.
Example:
Find out the Instantaneous Velocity of an object moving along a straight line for time t = 3s with a function x = 5t\[^{2}\] + 2t + 3?
Solution:
Known: The function of x = 5t\[^{2}\] + 2t + 3 2t
Differentiating the given function in reference to t, we get Instantaneous Velocity
V\[_{inst}\] = dx/dt
=d (5\[^{t2+2t+3}\]) / dt
V\[_{inst}\] = 10t + 2
For time t=3s,
Thus, the instantaneous velocity is V (t)= 10t + 2
V(3)=10(3)+ 2
V(3) =32 m/s
Instantaneous Velocity for the function is 32m/s.
For more instantaneous velocity examples refer to the Vedantu e-portal.
FAQs on Instantaneous Velocity Formula
Q1. What is the Concept of Instantaneous Velocity?
Answer: In mathematics, the instantaneous velocity is the rate of change of position for a time interval that is very short i.e. almost zeros (0). It is measured considering the SI unit ms−1. In addition, instantaneous speed implies the magnitude of the Instantaneous velocity. It consists of the same value as that of instantaneous velocity, with one difference that it does not possess any direction.
Q2. What are Some of the Common Mistakes and Misconceptions Associated with Instantaneous Velocity?
Answer: You know how to find instantaneous velocity or how to calculate instantaneous velocity. But we also need to know how to avoid common errors while finding instantaneous velocity. Following are a few misconceptions:-
Some people have a perception that instantaneous velocity and speed are similar to that average velocity and speed.
When people use the words velocity or speed, they generally mean instantaneous velocity or instantaneous speed. Average velocity and speed are reckoned for motion taking place over a time period, while instantaneous velocity and speed explain motion at a given moment in time.
