# 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:

$Instaneous\;&space;Velocity&space;=&space;Lim_{\Delta&space;t&space;}->0\frac{\Delta&space;x}{\Delta&space;t}=\frac{d&space;x}{d&space;t}$

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 = 5t2 + 2t + 3?

Known: The function is x = 5t2 + 2t + 3 2t
Distinguishing the given function with respect to t, we get Instantaneous Velocity

$V_{inst}=\frac{dx}{dt}$

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

=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 = 4t2 + 10t + 6. Compute its Instantaneous Velocity at time t = 5s.

Given: The function is x = 4t+ 10t + 6.
Differentiating the provided function with respect to t, we get

$V_{inst}=\frac{dx}{dt}$

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

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.