Instantaneous Velocity Calculator

Instantaneous Velocity Calculator

This instantaneous velocity calculator is used to calculate the velocity of an object at a particular instance for the given displacement and time. 

What is Instantaneous Velocity?

"A velocity of an object at a given moment in time"

When an object moves with a uniform velocity, then its instantaneous velocity will be equal to the standard velocity. 

How to Calculate Instantaneous Velocity?

It can be calculated using a formula that shows the instantaneous velocity which is the limit of the average velocity when the time interval tends towards zero. 

Instant Velocity Formula:

Instantaneous Velocity = Lim_{Δt → 0} x(t + Δt) - x(t) Δt

From the equation:

Instantaneous Velocity = dx (t) dt

Where:

• Δt = Smallest interval of the time
• x = Displacement 
• t = Time
• d  = Derivative of the position function

Example:

Suppose a car is moving along a straight path. Find how fast it is going at a specific moment by having a time of 3 seconds.

Car position is given by a function as:

x(t) = 5t² + 2t + 4

Solution:

Step # 1: Use the Instantaneous velocity formula:

v_int = dx(t) dt

Step # 2: Put the values into the formula:

v_int = d(5t² + 2t + 4) dt

Step # 3: Simplify the derivative

v_int = 10t + 2

Put the value of (t)

v_int = (10 * 3) + 2 

v_int= 32 ms^-1

Hence, at 3 seconds the instantaneous velocity of a car is 32 ms^-1. This means that the car’s position is changing at a rate of 32 meters every second at a specific moment. 

Difference between Instantaneous Speed & Instantaneous Velocity:

➥ Instantaneous Speed:

Instantaneous speed is said to be the magnitude of instantaneous velocity

• Scalar quantity
• Formula of instantaneous speed is: 

Speed_int = ds dt

➥ Instantaneous Velocity:

Instantaneous velocity is the change of position which takes place at a small change in time

• Vector quantity
• Formula of instantaneous velocity is: 

V_int = dx dt