Your Result is copied!

ADVERTISEMENT

Enter the values, and click on the “Calculate” button to find the instantaneous velocity of an object.

Add this calculator to your site

ADVERTISEMENT

ADVERTISEMENT

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

**"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.

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

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) = 5t^{2} + 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(5t^{2} + 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.

**➥ 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

**Support**

**Email us at**

© Copyrights 2024 by Calculator-Online.net