Scalar and Vector Quantities

Jamie Z 2024-06-16

Learning Goals

• Explain the difference between scalars and vectors
• Explain the difference between distance and displacement

Frame of Reference

• In each scenario mentions, the person’s point of view may differ
• In physics, determining the frame of reference let’s you establish our point of view of the direction

Scalars

Scalars are quantities which are described by magnitude alone

Vectors

Vectors are quantities which are described by both magnitude and a direction

Distance VS Displacement

• Distance is a scalar quantity that refers to how far an object travels during its motion
• Displacement is a vector quantity that refers the object's overall change in position from the origin

Velocity VS Speed

Just like distance and displacement, speed and velocity are also different.

• Speed (s) is a scalar quantity that refers to the rate of change in distance (how fast the object is moving). It does not consider the direction of the motion.
• Velocity (v) is the vector quantity of the rate at which an object changes its displacement. In other words, it is speed in a given direction.

Formulas

\[ s = \frac{d}{t} \]

• S = Speed

• D = Distance

• T = Time

  \[ v = \frac{s}{t} \]

• V = Velocity

• S = Speed

• T = Time

Converting To SI units

Acceleration

Acceleration (a) is the rate of change in velocity of an object

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

Where

• a = Acceleration (\(m/s^2\))
• v = Final Velocity (\(m/s)\)
• u = Initial Velocity (\(m/s)\)
• t = Time taken (s)