Calculator Online

Home AI Chat AI Math Solver

NEW

Tools ▾ Category ▾

Pricing Sign In

Calculator Online

Your Result is copied!

Change in Momentum Calculator

Select an option from the list, enter the values in the online calculator, and the tool will instantly determine the change in momentum at any moment.

Select Option:

$$\Delta P=m(V_f - {V_i})$$

$$\Delta P =m\Delta V$$

$$\Delta P =F.T$$

Force

kg ▾

Final Velocity

m/s ▾

Initial Velocity

m/s ▾

Related

The change in momentum calculator is a simple tool that determines how much an object’s momentum varies when its velocity changes. Since momentum depends on both mass and velocity, any variation in speed or direction results in a measurable momentum change.

How to Find Change in Momentum?

The change in momentum is calculated by subtracting the initial momentum from the final momentum of an object. Whenever velocity changes — either in magnitude or direction — momentum also changes.

Change in Momentum Formula:

The standard equation for change in momentum is:

Δp = m × Δv

If we expand this using initial and final velocities:

Δp = p₂ − p₁ = m v₂ − m v₁

This means we multiply the mass by the difference between final and initial velocity. The result gives the total momentum change of the object. A change in direction also contributes to Δp since momentum is a vector quantity.

What is Impulse?

Impulse refers to the effect of a force acting over a time interval. It is represented by the symbol J and is directly equal to the change in momentum.

J = F × t

Because impulse equals momentum change:

J = Δp

The unit of impulse is Newton-second (N·s), which is equivalent to kg·m/s. Therefore, impulse and change in momentum describe the same physical quantity from different perspectives.

Practical Example:

Consider an object of mass 80 kg that increases its speed from 4 m/s to 9 m/s in 5 seconds.

Given:

Initial velocity (u) = 4 m/s

Final velocity (v) = 9 m/s

Mass (m) = 80 kg

Time (t) = 5 s

Solution:

Initial momentum:

p₁ = m × u = 80 × 4 = 320 kg·m/s

Final momentum:

p₂ = m × v = 80 × 9 = 720 kg·m/s

Change in momentum:

Δp = p₂ − p₁

Δp = 720 − 320

Δp = 400 kg·m/s

To calculate the average force applied:

F = Δp / t

F = 400 / 5

F = 80 N

Summary:

Initial momentum = 320 kg·m/s

Final momentum = 720 kg·m/s

Change in momentum = 400 kg·m/s

Applied force = 80 N

How to Find Momentum Using Force and Time?

Newton’s second law states:

F = ma

Acceleration is defined as:

a = Δv / t

Substituting into Newton’s law:

F = m (Δv / t)

Since Δp = m Δv, we get:

F = Δp / t

Rearranging gives:

Δp = F × t

This shows that the change in momentum equals the force applied multiplied by the time interval. The calculator uses this principle to determine momentum variations efficiently.