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Instantaneous Velocity Calculator
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Instantaneous Velocity is the velocity of a particle at any instant of time. Instantaneous Velocity Calculator calculates the velocity covered by a body at any given instant of time.

Default function is given in the calculator to calculate the instantaneous velocity below. When you click on "Calculate Instantaneous velocity", instantaneous velocity is calculated by differentiating the function as per the formula shown in the steps and substituting the value.

## Steps for Instantaneous Velocity Calculator

Step 1 :

Read the problem and list the given parameters.

Step 2 :

There are two formulas used here:

If time fuction is given and you are interested in finding instantaneous Velocity then differentiate it as

V = $\frac{dx}{dt}$

Where V = Instantaneous Velocity,

x = Distance Covered

t = time taken.

If Initial and final quantities of Velocity and time are given then use the formula:

V = $\frac{x_{2} - x_{1}}{t_{2} - t_{1}}$

Where x2 = Final displacement,

x1 = Initial displacement,

t1 = Initial time,

t2 = Final time

Substituting the given quantities and get the answer.

## Problems on Instantaneous Velocity Calculator

1. ### If the body is moving with the time function is given as x(t) = t3 + 3t2 + 5 and time interval t = 2 s. Calculate its Instantaneous Velocity.

Step 1 :

Given: The time function is:

x(t) = t3 + 3t2 + 5 and t = 2 s.

Step 2 :

The Instantaneous Velocity is

V = $\frac{dx}{dt}$

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

= 3t2 + 6t .

At t = 2 s, the Instantaneous Velocity is:

V = 3 (2)2 + 6(2)

= 12 + 12

= 24 m/s.

The Instantaneous Velocity is 24 m/s.

2. ### Calculate the instantaneous velocity of a bicycle moving with initial Velocity 5m at the instant of 4th s and 7m at the instant of 6th s. Calculate its Instantaneous Velocity.

Step 1 :

given: x1 = 5m,
x2 = 7m,
t1 = 4s,
t2 = 6s.

Step 2 :

The Instantaneous Velocity is given by
V = $\frac{(x_{2} - x_{1})}{(t_{2} - t_{1})}$
= $\frac{(7 - 5)}{(6 - 4)}$

= $\frac{2}{2}$ m/s.