Momentum and Velocity Calculator

What is Momentum and Velocity?

Momentum is a measure of the motion of an object, combining both its mass and velocity. Velocity is a vector quantity that describes the rate of change of an object's position, including both speed and direction. These concepts are fundamental in physics and are closely related.

Formula

The relationship between momentum and velocity is expressed by the following equation:

\[ \vec{p} = m\vec{v} \]

Where:

• \(\vec{p}\) is the momentum vector (measured in kg⋅m/s)
• \(m\) is the mass of the object (measured in kg)
• \(\vec{v}\) is the velocity vector (measured in m/s)

Calculation Steps

Let's calculate the velocity of an object with a mass of 5 kg and a momentum of 20 kg⋅m/s:

1. Identify the known values:
   • Momentum, \(p = 20\) kg⋅m/s
   • Mass, \(m = 5\) kg
2. Rearrange the formula to solve for velocity: \[ v = \frac{p}{m} \]
3. Substitute the known values: \[ v = \frac{20 \text{ kg⋅m/s}}{5 \text{ kg}} \]
4. Perform the calculation: \[ v = 4 \text{ m/s} \]

Example and Visual Representation

Let's visualize the relationship between momentum, velocity, and mass:

This visual representation illustrates:

• The velocity of the object (4 m/s) represented by the blue arrow
• The mass of the object (5 kg) represented by the green square
• The momentum (20 kg⋅m/s) represented by the red dashed line
• The relationship between momentum, mass, and velocity illustrated by the purple arrow