Use graphs, vectors, and calculus relationships to connect position, velocity, and acceleration.
Complete Lesson Content
Scalars, Vectors, and One-Dimensional Motion
Build the foundation of motion description: scalars vs vectors, displacement vs distance, velocity vs speed, and how to choose a reference frame.
When we describe how something moves, words like "fast" or "far" are not enough for physics. We need quantities that carry both size and direction, and a rule for measuring them consistently.
This lesson introduces scalars (numbers only), vectors (numbers with direction), and how to use them to describe one-dimensional motion.
A scalar is a single number with a unit, such as 5 kg or 20 C. A vector has both magnitude and direction. In one dimension, direction is captured by a sign: positive or negative relative to a chosen positive direction.
- Scalar examples: mass, temperature, speed, distance, time.
- Vector examples in 1D: displacement, velocity, acceleration.
- In 1D, a vector is a signed number: +3 m/s means 3 m/s in the positive direction.
Speed is magnitude of velocity
Distance counts every meter traveled, regardless of direction. Displacement only cares about the starting point and the ending point.
If you walk 3 m forward and 2 m backward, distance = 5 m but displacement = +1 m (assuming forward is positive).
Displacement
Distance
Average velocity = displacement / time. Average speed = total distance / time. These can be very different.
Average velocity
Average speed
Classroom Check: displacement and velocity
A runner goes 100 m east in 20 s, then turns around and runs 60 m west in 15 s. Taking east as positive, which statement is correct?
- Treating velocity and speed as the same thing.
- Forgetting that displacement can be zero even when distance is large.
- Not choosing a positive direction before assigning signs.
- Using total distance instead of displacement when calculating average velocity.
Displacement
Average velocity
Average speed
Speed from velocity