Particle Acceleration Calculator

Formulas

To calculate the Particle Acceleration (PA):

Using velocity method:

\[ PA = \frac{v - u}{t} \]

Where:

\(PA\) is the Particle Acceleration (m/s²)
\(v\) is the final velocity (m/s)
\(u\) is the initial velocity (m/s)
\(t\) is the time interval (s)

Using force method:

\[ PA = \frac{F}{m} \]

Where:

\(PA\) is the Particle Acceleration (m/s²)
\(F\) is the force (N)
\(m\) is the mass (kg)

What is Particle Acceleration?

Particle acceleration refers to the rate of change of velocity of a particle with respect to time. It is a vector quantity, meaning it has both magnitude and direction. The units for particle acceleration in the International System of Units (SI) are meters per second squared (m/s²).

Example Calculation 1

Let's assume the following values:

Initial Velocity (\(u\)) = 10 m/s
Final Velocity (\(v\)) = 30 m/s
Time Interval (\(t\)) = 5 seconds
Force (\(F\)) = 100 Newtons
Mass (\(m\)) = 20 kg

Using the velocity method:

Step 1: Calculate the difference between final and initial velocities:

\[ v - u = 30 - 10 = 20 \text{ m/s} \]

Step 2: Divide by the time interval:

\[ PA = \frac{20}{5} = 4 \text{ m/s²} \]

Using the force method:

Step 1: Divide the force by the mass:

\[ PA = \frac{100}{20} = 5 \text{ m/s²} \]

The Particle Acceleration is 4 m/s² using the velocity method and 5 m/s² using the force method.

Example Calculation 2

Let's assume the following values:

Initial Velocity (\(u\)) = 5 m/s
Final Velocity (\(v\)) = 15 m/s
Time Interval (\(t\)) = 2 seconds
Force (\(F\)) = 200 Newtons
Mass (\(m\)) = 25 kg

Using the velocity method:

Step 1: Calculate the difference between final and initial velocities:

\[ v - u = 15 - 5 = 10 \text{ m/s} \]

Step 2: Divide by the time interval:

\[ PA = \frac{10}{2} = 5 \text{ m/s²} \]

Using the force method:

Step 1: Divide the force by the mass:

\[ PA = \frac{200}{25} = 8 \text{ m/s²} \]

The Particle Acceleration is 5 m/s² using the velocity method and 8 m/s² using the force method.