Let us Consider a cyclist riding, his velocities varies continuously depending on time, distance etc. At any particular instant if we want to find his velocity its nothing but instantaneous velocity.

**Instantaneous Velocity Formula** is used to determine the instantaneous velocity of the given body at any particular instant. It is given as:

Where**x **is the given function with respect to time **t**. The Instantaneous Velocity is expressed in **m/s**. If any problem contains the function of the form ** f(x)**, the instantaneous velocity is determined using the above formula.

Where

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Below are some problems based on instantaneous velocity which helps to understand the formula better.

Given: The function is x = 5t

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

V

= $\frac{d(5t^{2} + 2t + 3)}{dt}$

= 10t + 2

For time t = 3s, the Instantaneous Velocity is V(t) = 10t + 2

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

Instantaneous Velocity for the given function is 32m/s.

Given: The function is x = 4t

Differentiating the given function with respect to t, we get

V

= $\frac{d(4t^{2} + 10t + 6)}{dt}$

= 8t + 10.

For time t = 5s, the Instantaneous Velocity is V(t) = 8t + 10

V(5) = 8(5) + 10 = 50 m/s.

Instantaneous Velocity for the given function is 50 m/s.