Instantaneous Velocity Calculator

Enter the values and click the 'Calculate' button to determine the instantaneous velocity of an object.

Position function, x(t):

Evaluate at time, t₀:

Related

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?

"The velocity of an object at a specific 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.

Instantaneous Velocity Formula:

Instantaneous Velocity = LimΔt → 0 x(t + Δt) - x(t) Δt

Equivalent derivative form:

Instantaneous Velocity = dx (t) dt

Where:

Δt = Infinitesimally small time interval
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: Substitute the position function:

v_int = d(5t² + 2t + 4) dt

Step #3: Compute the derivative:

v_int = 10t + 2

Step #4: Substitute t = 3 s:

v_int = (10 × 3) + 2

v_int = 32 m/s

Thus, at 3 seconds, the instantaneous velocity of the car is 32 m/s. This indicates the car's position changes at a rate of 32 meters per second at that instant.