Unit 1.2: Displacement, Velocity, and Acceleration

Introduction

In this section, we introduce displacement, velocity, and acceleration—fundamental concepts in kinematics. Unlike distance, which is a scalar quantity, displacement is a vector that accounts for direction. Velocity describes motion with both speed and direction, while acceleration explains how velocity changes over time. These concepts are essential for solving motion problems in AP Physics.

Key Concepts

Displacement (\(\Delta x\)): The change in position of an object. Given by:
Displacement = Final Position - Initial Position
Velocity (\(v\)): The rate of change of displacement. Average velocity formula:
\( v = \frac{\Delta x}{\Delta t} \)
Acceleration (\(a\)): The rate of change of velocity. Average acceleration formula:
\( a = \frac{\Delta v}{\Delta t} \)

Tip: Always pay attention to signs in kinematics problems. Negative displacement, velocity, or acceleration often indicates motion in the opposite direction.

Graphical Representations

Understanding motion graphs is critical for solving AP Physics problems. Pay attention to the following:

Position vs. Time Graphs: The slope represents velocity.
Velocity vs. Time Graphs: The slope represents acceleration. The area under the graph represents displacement.
Acceleration vs. Time Graphs: The area under the graph represents change in velocity.

Exam Strategy: If a graph is given, analyze slopes and areas to determine motion properties.

Mathematical Routines

Mastering kinematic equations is essential. The three primary equations for constant acceleration are:

\( v = v_0 + at \)
\( x = x_0 + v_0 t + \frac{1}{2} a t^2 \)
\( v^2 = v_0^2 + 2a \Delta x \)

Tip: Choose the right equation based on what is known and what is unknown. Identify missing variables and select an equation that does not require them.

Practice Activities

Activity 1: Calculating Displacement

A car moves from \( x = -3m \) to \( x = 7m \). What is the displacement? Explain why displacement is different from distance traveled.

Activity 2: Average Velocity Calculation

A sprinter runs 100 meters north in 10 seconds, then immediately turns and runs 50 meters south in 5 seconds. What is the sprinter’s average velocity over the entire motion?

Activity 3: Graph Interpretation

Given a velocity vs. time graph with a straight-line slope, determine the acceleration and displacement over a 5-second interval.

Summary & Exam Preparation Tips

Mastering displacement, velocity, and acceleration is crucial for understanding motion in physics. Key takeaways include:

Displacement is a vector, while distance is a scalar.
Velocity describes both speed and direction.
Acceleration tells how velocity changes over time.
Graphs help visualize motion—slopes represent rates of change, and areas under graphs represent accumulated quantities.

Regular practice with kinematic equations and motion graphs will strengthen problem-solving skills for AP Physics exams.