Post-Collision Speed Calculator (Momentum)

Determine the final velocity of two objects after a perfectly inelastic collision using the law of conservation of momentum.

Unit System

Variables Table

Variable	Symbol	Meaning	Unit (SI)
Mass of Object 1	m₁	The amount of matter in the first object.	kg
Initial Velocity of Object 1	v₁ᵢ	The speed and direction of the first object before collision.	m/s
Mass of Object 2	m₂	The amount of matter in the second object.	kg
Initial Velocity of Object 2	v₂ᵢ	The speed and direction of the second object before collision.	m/s
Final Velocity	v𝒻	The common velocity of both objects after they stick together.	m/s

What is Calculating Post-Collision Speed Using Momentum?

Calculating post-collision speed using momentum is a fundamental application of physics, specifically the law of conservation of momentum. This law states that for an isolated system (one with no external forces acting on it), the total momentum before a collision is equal to the total momentum after the collision. This calculator deals with a specific type of interaction known as a “perfectly inelastic collision,” where the colliding objects stick together and move as a single mass after impact.

This principle is crucial in accident reconstruction, engineering safety tests, and understanding physical interactions from the cosmic scale (galaxy mergers) to the subatomic (particle collisions). By knowing the masses and initial velocities of the objects, we can precisely predict their shared velocity after they collide and combine.

The Formula for Post-Collision Speed (Inelastic Collision)

The conservation of momentum provides a powerful and straightforward formula for this calculation. The total momentum before the collision is the sum of the individual momenta of each object (where momentum `p` is mass `m` times velocity `v`). After the collision, the total momentum is the combined mass moving at a single final velocity.

The equation is:

(m₁ * v₁ᵢ) + (m₂ * v₂ᵢ) = (m₁ + m₂) * v𝒻

To find the final velocity (v𝒻), we rearrange the formula:

v𝒻 = (m₁v₁ᵢ + m₂v₂ᵢ) / (m₁ + m₂)

Where `m₁` and `m₂` are the masses of the objects, and `v₁ᵢ` and `v₂ᵢ` are their initial velocities, respectively. If you need more information about collisions, you might find an article on {related_keywords} at {internal_links} useful.

Practical Examples

Example 1: Rear-End Car Collision

Imagine a car (m₁ = 1500 kg) moving at 20 m/s (v₁ᵢ) rear-ends a stationary truck (m₂ = 4500 kg, v₂ᵢ = 0 m/s). They lock bumpers and move together.

• Inputs: m₁=1500 kg, v₁ᵢ=20 m/s, m₂=4500 kg, v₂ᵢ=0 m/s
• Initial Momentum of Car: 1500 kg * 20 m/s = 30,000 kg·m/s
• Initial Momentum of Truck: 4500 kg * 0 m/s = 0 kg·m/s
• Total Initial Momentum: 30,000 kg·m/s
• Total Mass: 1500 kg + 4500 kg = 6000 kg
• Final Velocity (v𝒻): 30,000 / 6000 = 5 m/s

The combined wreckage moves forward at 5 m/s.

Example 2: Football Tackle

A running back (m₁ = 95 kg) is running at 8 m/s (v₁ᵢ). A linebacker (m₂ = 110 kg) is running towards him from the opposite direction at -6 m/s (v₂ᵢ, negative because of opposite direction). They collide and stick together.

• Inputs: m₁=95 kg, v₁ᵢ=8 m/s, m₂=110 kg, v₂ᵢ=-6 m/s
• Initial Momentum of Running Back: 95 kg * 8 m/s = 760 kg·m/s
• Initial Momentum of Linebacker: 110 kg * -6 m/s = -660 kg·m/s
• Total Initial Momentum: 760 + (-660) = 100 kg·m/s
• Total Mass: 95 kg + 110 kg = 205 kg
• Final Velocity (v𝒻): 100 / 205 ≈ 0.49 m/s

The combined mass of the players moves slightly in the initial direction of the running back.

How to Use This Post-Collision Speed Calculator

1. Select Units: First, choose your preferred units for mass (kg or lb) and velocity (m/s or mph). The calculator handles all conversions automatically.
2. Enter Masses: Input the mass for Object 1 and Object 2 in the designated fields.
3. Enter Initial Velocities: Input the starting velocity for each object. Direction is critical! Use a positive value for one direction and a negative value for the opposite direction. A stationary object has a velocity of 0.
4. Review Results: The calculator instantly updates. The primary result is the Combined Final Velocity. You can also see intermediate values like the initial momentum of each object and the total mass.
5. Analyze the Chart: The bar chart provides a visual representation of the momentum before and after the collision, helping to understand the conservation principle. For further reading, check our guide on {related_keywords} here: {internal_links}.

Key Factors That Affect Post-Collision Speed

• Mass of Objects: The relative mass of the two objects is a primary determinant. A much heavier object will dominate the momentum equation, causing the final velocity to be closer to its initial velocity.
• Initial Velocity of Objects: Both speed and direction are critical. A head-on collision (velocities with opposite signs) can result in a much lower final speed, or even a change in direction, compared to a rear-end collision (velocities with the same sign).
• Direction of Impact: This calculator assumes a one-dimensional (head-on or rear-end) collision. In two or three dimensions, the angles of impact would be required to break down the velocity vectors into components.
• Type of Collision: This tool assumes a perfectly inelastic collision where objects stick together. In an elastic collision (where objects bounce off each other), kinetic energy is also conserved, leading to a different set of equations and outcomes. You can learn more about {related_keywords} at {internal_links}.
• External Forces: The law of conservation of momentum applies to isolated systems. Forces like friction or air resistance can affect the outcome in real-world scenarios, but are ignored in this idealized calculation for clarity.
• Loss of Mass: This calculation assumes all mass is conserved in the final object. In a real, violent collision, parts may break off, which would alter the “total mass” used in the final momentum calculation.

Frequently Asked Questions (FAQ)

1. What is momentum?
Momentum is often called “mass in motion.” It is a vector quantity, meaning it has both magnitude and direction, and is calculated as the product of an object’s mass and its velocity (p = mv).

2. Why is velocity negative in some examples?
Velocity is a vector. We use a one-dimensional coordinate system for simplicity. A positive velocity means movement in one direction (e.g., to the right), while a negative velocity indicates movement in the opposite direction (e.g., to the left). This is crucial for calculating the total momentum correctly.

3. What’s the difference between an elastic and inelastic collision?
In an elastic collision, both momentum and kinetic energy are conserved (think billiard balls bouncing off each other). In an inelastic collision, momentum is conserved, but some kinetic energy is converted into other forms, like heat, sound, or deformation of the objects. A perfectly inelastic collision (which this calculator models) is where the objects stick together, maximizing the loss of kinetic energy.

4. Can the final velocity be zero?
Yes. If the initial momenta of the two objects are equal in magnitude but opposite in direction, the total initial momentum is zero. (e.g., `m₁v₁ = -m₂v₂`). In this case, the objects will come to a complete stop upon collision.

5. Does this calculator work for 2D or 3D collisions?
No. This calculator is specifically for one-dimensional collisions (along a straight line). For 2D or 3D collisions, you would need to break down the initial velocity vectors into their x, y, and z components and apply the conservation of momentum principle to each axis independently. For more complex scenarios, consider our {related_keywords} page at {internal_links}.

6. What do the units “kg·m/s” mean?
This is the standard SI unit for momentum, representing kilograms times meters per second. It directly reflects the formula for momentum (mass × velocity).

7. What happens to the “lost” kinetic energy in an inelastic collision?
It is transformed into other energy forms. In a car crash, for example, it becomes the sound of the impact, the heat generated in the bending metal, and the energy required to deform and crumple the car’s body.

8. How do I handle different units like grams or kilometers per hour?
This calculator provides built-in converters for common units (kg/lb and m/s/mph). If you have other units, you must convert them to one of the supported systems before entering the values. For example, to convert grams to kilograms, divide by 1000.

Related Tools and Internal Resources

If you found this tool useful, you might also be interested in our other physics and engineering calculators. Explore more concepts to deepen your understanding.

• {related_keywords}: Calculate outcomes for collisions where objects bounce apart.
• {related_keywords}: Determine the energy of an object in motion.