Introduction

Welcome to the FiveHive article on Unit 1.1 of AP Physics 1!

In this article, we will go over scalars and vectors in one dimension. The information from this unit is essential for future topics in this course, such as forces, their components, and more. 

For now, we will only cover the topics highlighted in the CED for unit 1.1.

Defining Vectors and Scalars

Scalars are quantities that are described by only magnitude (or how “strong” the value is). Whereas, vectors are quantities that are described by using both magnitude AND direction. 

Some examples of scalars include speed, time, and mass because these values are described solely by their magnitude. Some examples of vectors include velocity, displacement, force, and acceleration because these values are described by magnitude and direction. 

Vector Representation

Vectors are represented using an arrow above the symbol for a quantity. However, when splitting vectors, such as velocity, the arrows are not necessary and the quantity can be represented by the axis that it represents (for example, $v_x$ or $v_y$).  Vectors can also be denoted by arrows. The length of the arrow depends on the magnitude of the quantity, and the direction depends on the sign of the quantity. 

Adding Scalars and Vectors

Scalar addition is quite simple, as you can simply add the values together due to the lack of direction. As a result, if you are adding two masses of $10\mathrm{kg}$ and $20\mathrm{kg}$, you may simply add the masses together to get $30\mathrm{kg}$. 

However, vector addition is more complicated due to the involvement of direction (and often, angles once we get to two dimensions). In one dimension, we have to account for whether an object has a positive or negative direction. 

Example 1:

A car travels $10\mathrm{m}$ north and quickly turns and travels $20\mathrm{m}$ south. What is the total displacement? 

In physics, the sign convention states that vectors to the right and up (east and north) are positive. Therefore, the $10\mathrm{m}$ displacement was positive and the $20\mathrm{m}$ displacement was negative. Adding the two vectors yields a displacement of $-10\mathrm{m}$ or $10\mathrm{m}$ to the south. 

In addition (get it? hehe) to adding vectors, you will also have to determine the type of motion of an object given the direction of the velocity vector and the direction of the acceleration vector. A rule of thumb in this topic is to see if both vectors are pointing in the same direction. If they are, the object is speeding up and if not, it is slowing down. If acceleration is $\text{0}$, the object has a constant velocity.

Practice

Practice what you have learned about vectors and scalars through the three questions below: