Introduction

Welcome to the FiveHive article for Unit 1.2 of AP Physics 1!

In this article, we will be exploring three different components of physics: displacement, velocity, and acceleration. Once again, this information will serve crucial purposes for various units in this course and in the following physics courses. 

As usual, we will only cover the topics included in the CED for unit 1.2.

Simplifications in Physics

Oftentimes in physics, we will make huge simplifications to make concepts and procedures easier to understand. One of the biggest and most well-known simplifications in physics is the negligible air resistance (unless otherwise mentioned). Furthermore, in this course, we will treat many objects as a single point by ignoring their size, shape, and internal configuration. We treat these point-like objects with extensive properties such as mass.

Displacement vs. Distance

Displacement and distance are often thought to be the same. However, there is a very important distinction between the two. As discussed in unit 1.1, distance is a scalar, and displacement is a vector. As a result, the direction of the displacement vector changes the magnitude as per the sign convention. 

In addition, displacement is also known as the straight-line distance between two points or the change in position of an object. 

The equation for displacement is given as such: $\Delta x=x_f-x_o$ 

Example: Consider a car that started at the origin, travelled $20\mathrm{m}$ to the north, turned around, and travelled $20\mathrm{m}$ to the south. The distance that this car covered is $40\mathrm{m}$. However, the displacement is $0\mathrm{m}$ because the car ended up where it began ($\Delta x=0-0=0$).

Velocity

Earlier in your education, you might have learned that speed is distance divided by time. The same principle applies to velocity, except instead of distance, we divide displacement by the change in time.

In equation form, ${\vec{v}}_{avg}=\frac{\Delta x}{\Delta t}$.

Similar to speed, the unit for average velocity is $\text{m/s}$. The difference is that while speed is simply distance divided by time, average velocity is the displacement divided by change in time. This way, average velocity also has direction, making it a vector.

Common Misconception! 

Oftentimes, students reduce the definition of velocity to “speed with direction”. However, this definition is incorrect, and it is extremely important to consider the fact that displacement is used in place of distance.

Acceleration

Using what we know about the velocity of an object, we can derive the object’s acceleration. To calculate average acceleration, we divide the change in an object’s velocity by the change in time. (Note: the fact that we are dividing change in velocity is an important observation for making conclusions about an object’s motion later on.) 

In equation form, average acceleration is written as: ${\vec{a}}_{avg}=\frac{\Delta v}{\Delta t}$. 

Since we are dividing change in velocity (which is in $\text{m/s}$) by change in time (which is in seconds), the unit for average acceleration is meters per second per second, or ${\text{m/s}}^2$.

An object is only considered to be accelerating if the magnitude and/or the direction of its velocity change. If none of the two change, that means the velocity is constant ($\Delta v=0$), and as a result, the acceleration is $0$ as well. 

Practice

You’ve made it through unit 1.2 of AP Physics 1! Yay! Now, it is time to put what you have learned in this unit to the test with some practice problems.