Vectors in Mechanics

This lesson covers the use of vectors in mechanics as required by the Edexcel 9MA0 A-Level Mathematics specification. You need to work with position vectors, velocity vectors and force vectors in two dimensions, using both column-vector and i-j notation.

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Vector Notation

In two dimensions, vectors can be written as:

• Column notation: v = (3, -2) or as a column
• i-j notation: v = 3i - 2j

where i is the unit vector in the x-direction and j is the unit vector in the y-direction.

The magnitude of v = ai + bj is:

|v| = √(a² + b²)

The direction (angle θ with the positive x-axis) is:

θ = arctan(b/a)

Exam Tip: When finding the direction, always draw a sketch to check which quadrant the vector is in. The arctan function only gives angles in the range -90° to 90°, so you may need to add or subtract 180°.

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Position, Velocity and Acceleration Vectors

If a particle has position vector r, velocity vector v and acceleration vector a:

v = dr/dt (differentiate each component with respect to t) a = dv/dt (differentiate again)