First and foremost, before knowing how to find instantaneous velocity from average velocity, we have to know about average and instantaneous velocity.

**The instantaneous velocity is considered the measure of a limit of V _{avg} as the time tends towards a specific value.**

**Average and instantaneous velocity differ as their name suggests; one is used to calculate total velocity, and the other is used to measure instant velocity.**

We’ll know the fundamental differences of the above two velocities before learning how to find instantaneous velocity from the average velocity.

**Average velocity: Points to remember**

Before going to the central concept, let us first know about the average velocity.

**Average velocity is one of the primary concepts used in physics to measure how much distance a particle covers in its motion during a specific period.****It is one of the main scalar physical quantities.****It has a dimension equal to length/time since it is measured using the area covered in a certain period.**

Now let’s have a look at instantaneous velocity

**Instantaneous velocity: Points to remember**

After knowing about average velocity, now it is mandatory to know about instantaneous velocity.

**Instantaneous velocity is the fundamental concept of physics that is used to find out the velocity of a particle, which is in motion at any particular point of time, using the position and time of that particle.****It is a primary vector quantity.****Even it has a dimension similar to average velocity [ Distance/time = L/T].**

Now let’s know how to find V_{inst} from V_{avg}, which is the post’s focus.

**How to find instantaneous velocity from** **average velocity**

Before measuring the instantaneous velocity of an object, it is necessary to find out its average velocity.

**In a distance-time graph, first, we have to measure average velocity by taking the two increments, i.e., one larger and one smaller increment of distance and time to a point for which we will measure V**_{inst}.**After this, we have to take the average of those smaller and larger points.****For this value, you have to consider the V**_{avg}formula and apply its limit at t equals any value of your choice. You will be able to find**V**._{inst}

Now let us know in detail how to find instantaneous velocity from average velocity by using the formula.

**From formula**

We will know how to find V_{inst} from V_{avg }step by step as given below.

**Step 1**

**Take a displacement equation of the form S.**

**Step 2**

**Consider the given two-time intervals for which you have to find the average velocity.**

**Step 3**

**Try to calculate the average velocity for those values with the help of the formula given below,**

**It can also** **be written as below,**

**Step 4**

**If you want to calculate instantaneous velocity, you have to apply a limit function to the average velocity formula.**

Now let us know in detail how to find instantaneous velocity from average velocity by using a graph.

**From graph**

The most straightforward method to find V_{inst} from V_{avg} is from the representation of the graph.

**Step 1**

**Use both the axes of the graph to represent position and time respectively on the x and y-axis.**

**Step 2**

**Consider any displacement equation and insert specific values for t and mark it as follows on the graph.**

** [ t, S (X, Y)]**

**Now consider any two points as (x, y)** **and (x _{1}, y_{1}) and name them as C and D.**

**Step 3**

**In step 3, you have to connect those two points through a line and measure** **the average velocity; one can use the below formula to calculate average velocity**.

**where K refers to the slope between C and D.**

**Step 4**

**The line drawn to the slope taken is considered to be a tangent line.**

**Repeat the same process as mentioned in step 3, and continue choosing the points closer to each other.**

**After several attempts, it reaches a single point on the tangent line.** **Repeat to find slope several times, moving D nearer to C. **

**If we take the limit to that single point, we can find out the value of the slope at that particular point.**

**Step 5**

**After all the above processes, you will get a time interval that is infinitely equal to K at point C.****This value is known as instantaneous velocity and is measured by taking the limit to the given function into consideration with time interval.**

Now it is time to solve some problems based on average and instantaneous velocity to understand them better.

**Problems to find instantaneous velocity from average velocity**

The problems that are solved below are some of the basic calculations to find V_{inst} from V_{avg} .

**Problem 1**

Find the average velocity equation for the given displacement function** ** S = -6t^{2} + 11t + 9 and even calculate the instantaneous velocity at t=7s?

**Solution:**

**The given displacement equation is as follows**

** S = -6t ^{2} + 11t + 9 **

**ds/dt = -(2) 6t ^{(2-1)} + (1)11t^{1 – 1} + (0)9t^{0}**

^{ }**ds/dt = -12t ^{1} + 11t^{0}**

**ds/dt = -12t + 11**

**This will be the equation to find the average velocity. Now, if we substitute the limit value t tends to 7s, we can calculate instantaneous velocity.**

**ds/dt = -12(7) + 11**

**ds/dt = -84 + 11**

** ds/dt = -73 meters/second**

Therefore, the instantaneous velocity is -73m/s.

**Problem 2**

The bus covers a distance of 48Km in 45 minutes, and the equation for** **the motion of the bus is given by the function S = 6t^{2} + 8t + 3. Find its average velocity and then compute its Instantaneous Velocity at time t = 8s?

**Solution:**

**First let us find average velocity**

**ds/dt = 48/45**

**V _{avg} = ds/dt = 1.066 m/s**

**The function is S = 6t ^{2 }+ 8t + 3.**

**Differentiate the given equation with respect to t, then we get**

**ds/dt = 12t + 8**

**For time t = 8s, the Instantaneous Velocity is articulated as,**

**V(t) = 12t + 8**

**V(5) = 12(8) + 8**

**V(5)= 104 m/s.**

Thus for the known function, Instantaneous Velocity is 104 m/s.

**Problem 3**

Find the average velocity at a given time interval of a kid when he moves 8 m in 5 s and 20 min 8 s along the horizontal axis?

**Solution:** **Initial distance traveled by the kid, x _{i} = 8 m,**

**Final distance traveled by the kid, x _{f} = 20 m**

**Initial time interval t _{i} = 5 s**

**Final** t**ime interval to = 8 s**

**Average velocity V = x _{i} − x_{f} / t_{i} − t_{f} = 20−8 / 8−5 = 12 / 3 = 4 m/s**

**Frequently asked questions | FAQs**

**What is the formula to measure instantaneous velocity?**

The formula used to measure instantaneous velocity can be taken as follows,

**As we know, both average and instantaneous velocity can be calculated in the same motion; then, we can find instantaneous velocity by using the same formula as average velocity but with the addition of a limit value.**

**Which** **graph is used to find instantaneous** **velocity from average velocity?**

The graph that helps know the velocities of an object is the Position-time graph.

**In a position-time graph, we can measure certain different concepts of physics. It is the primary graphs that help to measure instantaneous velocity, average velocity, speed, etc.**

**Are average speed and average velocity the same?**

Both average speed and average velocity are entirely different quantities.

**Speed, in general, refers to a scalar quantity that signifies only the magnitude of the object. In contrast, velocity refers to vector quantity that indicates both magnitude and direction of a body in motion. The word average refers to total calculation, whereas instantaneous refers to a particular moment.**