Angle Between Velocity and Acceleration Vectors Calculator

Calculate Angle Between Vectors











Formula

The formula to calculate the angle between the velocity and acceleration vectors is:

\[ A = \cos^{-1} \left( \frac{\mathbf{a} \cdot \mathbf{b}}{||\mathbf{A}|| \cdot ||\mathbf{B}||} \right) \]

Where:

What are Velocity and Acceleration Vectors?

Velocity and acceleration vectors are 3-Dimensional representations of the physical properties of velocity and acceleration. The velocity vector represents the speed and direction of an object, while the acceleration vector represents the rate of change of the velocity vector.

Example Calculation

Let's assume the following values:

Using the formula:

\[ \mathbf{a} \cdot \mathbf{b} = (3 \cdot 1) + (4 \cdot 2) + (0 \cdot 2) = 3 + 8 + 0 = 11 \] \[ ||\mathbf{A}|| = \sqrt{3^2 + 4^2 + 0^2} = \sqrt{9 + 16 + 0} = \sqrt{25} = 5 \] \[ ||\mathbf{B}|| = \sqrt{1^2 + 2^2 + 2^2} = \sqrt{1 + 4 + 4} = \sqrt{9} = 3 \] \[ A = \cos^{-1} \left( \frac{11}{5 \cdot 3} \right) = \cos^{-1} \left( \frac{11}{15} \right) = 42.27 \text{ degrees} \]

The angle between the vectors is 42.27 degrees.