Vectors, Motion, and Change

Manual: General · Subject: Theoretical Physics

How to describe direction, motion, and changing quantities.

Scalars and Vectors

Scalars vs vectors

A scalar has size only, like mass or temperature. A vector has size and direction, like velocity or force.

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Memory aid

If direction matters, think vector. If only amount matters, think scalar.

Motion

Motion is often described using position $x(t)$ , velocity $v(t)$ , and acceleration $a(t)$ . In one dimension, velocity is the rate of change of position: $v = \frac{dx}{dt}$ .

Change over time

Acceleration is the rate of change of velocity: $a = \frac{dv}{dt}$ . If acceleration is positive, velocity is increasing in the chosen direction.

Which of the following is a vector?

Temperature Mass Velocity Time

Write the mathematical definition of acceleration in one variable.

Describing motion in one dimension

1

Choose a coordinate axis.
2

Write position as a function of time.
3

Differentiate position to get velocity.
4

Differentiate velocity to get acceleration.

If position is changing faster and faster, which quantity is increasing most directly?

Acceleration Mass Temperature Charge

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