Instantaneous Velocity Calculator

Calculate the instantaneous velocity of an object using this instantaneous velocity calculator. Enter the initial velocity, acceleration, and time elapsed to calculate the velocity at a given time. This calculator can evaluate the initial velocity, time, or acceleration, given the other variables are known (assuming constant acceleration over the time interval).

Instantaneous Velocity Calculator

Enter any 3 values to calculate the missing variable (assumes constant acceleration)

Initial Velocity m/s km/h mph ft/s Time s min h Acceleration m/s² km/h² ft/s² Instantaneous Velocity m/s km/h mph ft/s Calculate Reset

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Instantaneous Velocity Formula

The following formula can be used to calculate the velocity of an object at any given time when the acceleration is constant, assuming the initial time is t = 0.

v_t = v_0 + a t

• Where vt is the velocity at time t (the instantaneous velocity at that instant)
• v0 is the initial velocity
• t is time elapsed
• and a is (constant) acceleration

To calculate the velocity at time t (under constant acceleration), multiply the acceleration by time, then add the result to the initial velocity.

Instantaneous Velocity Definition

Instantaneous velocity is a term in physics used to describe the rate of change of displacement (position) with respect to time at a specific instant. An object undergoing acceleration will generally have different instantaneous velocities at different times because acceleration is the rate of change of velocity.

Instantaneous velocity can be found in different ways. For example, you can calculate it using kinematics equations like v = v0 + at when acceleration is constant. More generally, velocity is the derivative of position with respect to time (v(t) = dx/dt). If acceleration is known as a function of time, velocity can be found by integrating acceleration: v(t) = v0 + ∫0t a(τ) dτ.

The other method to estimate instantaneous velocity is through measurement using devices like a speedometer. This is often done for things like measuring the speed of a car or other moving vehicles.

How to calculate instantaneous velocity

The following example is a step-by-step guide on how to calculate the instantaneous velocity of an object. For this example, we will assume an object has an initial velocity and a constant acceleration.

1. First, we must measure the initial velocity. We will say for this example that this is a car moving along the street. At a time of t=0 seconds, we find the car to be moving at 30 m/s.
2. Next, we must determine the acceleration of the car. To simplify the problem, we will assume that we know the acceleration, as calculating it from the force of the engine and other factors would be a problem on its own. We find the acceleration is 5 m/s².
3. Now, the total time that has passed needs to be determined. For this example, 10 seconds have passed.
4. Finally, enter the information into the formula above. v = 30 m/s + (5 m/s²)(10 s) = 80 m/s.
5. Analyze the results and apply them to future problems.

FAQ

What is an instantaneous velocity?

Instantaneous velocity is a term in physics used to describe the rate of change of displacement (position) with respect to time at a specific instant. An object undergoing acceleration will generally have different instantaneous velocities at different times because acceleration is the rate of change of velocity.