**Instantaneous Velocity Formula**

Let us imagine a cyclist riding; his velocities differs unceasingly dependent on distance, time etc. At one particular moment if we want to find his velocity it’s not anything but instantaneous velocity.**Instantaneous Velocity Formula** is made use of to determine the instantaneous velocity of the given body at any specific instant. It is articulated as:

Where with respect to time **t, x **is th=e given function. The Instantaneous Velocity is articulated in **m/s**. If any numerical contains the function of form **f(x)**, the instantaneous velocity is calculated using the overhead formula.

**Instantaneous Velocity Solved Examples**

Underneath are some numerical grounded on instantaneous velocity which aids in understanding the formula properly.

**Problem 1: **Calculate the Instantaneous Velocity of a particle traveling along a straight line for time t = 3s with a function x = 5t^{2} + 2t + 3?

**Answer:**

Known: The function is x = 5t^{2} + 2t + 3 2t

Distinguishing the given function with respect to t, we get Instantaneous Velocity

=10t + 2

For time t=3s, the instaneous velocity is V(t)= 10t + 2

V(3)=10(3)+ 2=32m/s

instaneous Velocity for the given function is 32m/s

**Problem 2: **The motion of the car is provided by the function x = 4t^{2} + 10t + 6. Compute its Instantaneous Velocity at time t = 5s.

**Answer:**

Given: The function is x = 4t^{2 }+ 10t + 6.

Differentiating the provided function with respect to t, we get

For time t = 5s, the Instantaneous Velocity is articulated as,

V(t) = 8t + 10

V(5) = 8(5) + 10

= 50 m/s.

Thus for the known function, Instantaneous Velocity is 50 m/s.