---
title: "AP Physics 1 1.2: Displacement, Velocity, and Acceleration"
description: "Review AP Physics 1 Topic 1.2, including displacement, velocity formula, average velocity, average acceleration, distance vs displacement, instantaneous velocity, vector signs, and acceleration from changing speed or direction."
canonical: "https://fiveable.me/ap-physics-1-revised/unit-1/2-displacement-velocity-and-acceleration/study-guide/HyscWF2F28uakfpc"
type: "study-guide"
subject: "AP Physics 1"
unit: "Unit 1 – Kinematics"
lastUpdated: "2026-06-09"
---

# AP Physics 1 1.2: Displacement, Velocity, and Acceleration

## Summary

Review AP Physics 1 Topic 1.2, including displacement, velocity formula, average velocity, average acceleration, distance vs displacement, instantaneous velocity, vector signs, and acceleration from changing speed or direction.

## Guide

Displacement is the change in an object's [position](/ap-physics-1-revised/key-terms/position "fv-autolink"), a [vector](/ap-physics-1-revised/key-terms/vector "fv-autolink") you find with $\Delta x = x - x_0$. Average velocity is displacement divided by time, and average acceleration is the change in velocity divided by time.

## Why This Matters for the AP Physics 1 Exam

Displacement, velocity, and acceleration are the building blocks for everything in [kinematics](/ap-physics-1-revised/unit-1 "fv-autolink") and beyond. Once you can describe how an object's position changes and how fast that change happens, you can reason through [forces](/ap-physics-1-revised/unit-2/2-forces-and-free-body-diagrams/study-guide/jQ2Obd0dAU4QiTPN "fv-autolink"), energy, and momentum later in the course.

On the [AP Physics 1](/ap-physics-1-revised "fv-autolink") exam, you will see these ideas in multiple-choice questions that ask you to compare [distance](/ap-physics-1-revised/key-terms/distance "fv-autolink") with displacement, interpret motion descriptions, and calculate averages from given data. Building motion representations and translating between them is a core skill, so getting comfortable with the vector definitions here pays off when you reach graphs and equations in later topics.

## Key Takeaways

- Displacement is a vector found with $\Delta x = x - x_0$, while distance is the total path length and is always positive.
- Average velocity is $\vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t}$, and average acceleration is $\vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t}$.
- An object is accelerating if the [magnitude](/ap-physics-1-revised/key-terms/magnitude "fv-autolink") or direction of its velocity changes, so turning at constant [speed](/ap-physics-1-revised/key-terms/speed "fv-autolink") still counts as accelerating.
- The [object model](/ap-physics-1-revised/key-terms/object-model "fv-autolink") treats an object as a single point with properties like [mass](/ap-physics-1-revised/key-terms/mass "fv-autolink"), ignoring size, shape, and internal structure.
- Averaging velocity or [acceleration](/ap-physics-1-revised/unit-1/5-vectors-and-motion-in-two-dimensions/study-guide/LvdiAzU3amzMqu6O "fv-autolink") over a very small time interval gives a value close to the instantaneous value.
- Watch your signs: in one dimension, the sign of a [vector component](/ap-physics-1-revised/unit-1/1-scalars-and-vectors-in-one-dimension/study-guide/4jyE1aiM5EBRDi9A "fv-autolink") shows its direction.

## Core Concepts

### The object model

When studying motion, you treat an object as a single point, ignoring its size, shape, and internal structure. The point still carries properties like mass and charge. This keeps the analysis focused on the motion of the whole object instead of how each piece moves.

For example, when analyzing the path of a baseball, you do not track how the stitches rotate. You treat the entire ball as one point with mass.

### Displacement

Displacement measures how far out of position an object ends up compared to where it started. It only cares about the straight-line difference between the start and end positions, not the path taken to get there.

- Displacement is the change in an object's position.
- Relevant equation: $\Delta x = x - x_0$
  - $\Delta x$ is the displacement
  - $x$ is the final position
  - $x_0$ is the initial position
- Displacement is a vector, so it can be positive, negative, or zero depending on direction.

Distance is different. Distance is the total path length and is always positive. If you walk 3 meters east then 4 meters north, your displacement is 5 meters northeast, but the distance you walked is 7 meters.

### Average velocity

Average velocity tells you how quickly position changes over a time interval, including direction. Because it has direction, velocity is a vector, which separates it from speed.

- Average velocity is displacement divided by the time interval.
- Relevant equation: $\vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t}$
- Units are meters per second (m/s).

A train that travels 30 km east in 45 minutes has an average velocity of 40 km/h east, telling you both how fast and which way it moved.

### Average acceleration

Average acceleration describes how quickly velocity changes over a time interval. Like velocity, it is a vector.

- Average acceleration is the change in velocity divided by the time interval.
- Relevant equation: $\vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t}$
- Units are meters per second squared (m/s²).

A rocket that goes from rest to 200 m/s in 10 seconds has an average acceleration of 20 m/s², meaning its velocity grows by 20 m/s each second.

### When is an object accelerating?

An object accelerates whenever the magnitude or direction of its velocity changes.

- A change in magnitude means speeding up or slowing down.
- A change in direction means turning, even at constant speed.
- An object with [constant velocity](/ap-physics-1-revised/key-terms/constant-velocity "fv-autolink") (same size and direction) is not accelerating.

A car moving around a circular track at constant speed is still accelerating, because its velocity keeps changing direction as it points tangent to the circle.

### Average versus instantaneous values

Average values describe motion over an interval, while instantaneous values describe motion at a single moment. Calculating average velocity or average acceleration over a very small time interval gives a value very close to the instantaneous value at that instant.

For a ball thrown straight up, the [instantaneous velocity](/ap-physics-1-revised/key-terms/instantaneous-velocity "fv-autolink") at its highest point is zero, even though its average velocity over the whole trip is not.

## How to Use This on the AP Physics 1 Exam

### Problem Solving

- Identify initial and final states first. Most calculations here come down to a final value minus an initial value over a time interval.
- Keep direction attached to your answer. Velocity, acceleration, and displacement are vectors, so include a sign or compass direction.
- Track units carefully: m/s for velocity, m/s² for acceleration.

### Common Trap

- Do not mix up distance and displacement. A round trip can have a large distance but zero displacement.
- Slowing down does not always mean negative acceleration. The sign depends on direction relative to your chosen positive axis, not on whether the object speeds up or slows down.

## Practice Problem 1: Displacement Calculation

> A hiker walks 3 km east, then 4 km north, and finally 1 km west. Calculate the hiker's displacement from the starting point. What is the difference between the displacement and the total distance traveled?

To solve this problem, we need to find the net displacement vector from the starting point to the final position.

First, let's identify the individual displacements:
- 3 km east: +3 km in x-direction
- 4 km north: +4 km in y-direction
- 1 km west: -1 km in x-direction

Net displacement in x-direction: 3 km - 1 km = 2 km east

Net displacement in y-direction: 4 km north

Using the [Pythagorean theorem](/ap-physics-1-revised/key-terms/pythagorean-theorem "fv-autolink") to find the magnitude of the displacement:
$$|\Delta \vec{r}| = \sqrt{(2 \text{ km})^2 + (4 \text{ km})^2} = \sqrt{4 \text{ km}^2 + 16 \text{ km}^2} = \sqrt{20 \text{ km}^2} = 4.47 \text{ km}$$

The direction can be found using trigonometry:
$$\theta = \tan^{-1}(\frac{4 \text{ km}}{2 \text{ km}}) = \tan^{-1}(2) = 63.4° \text{ north of east}$$

Therefore, the displacement is 4.47 km at 63.4° north of east.

The total distance traveled is simply the sum of the distances for each segment:
$$\text{Total distance} = 3 \text{ km} + 4 \text{ km} + 1 \text{ km} = 8 \text{ km}$$

The difference between displacement (4.47 km) and total distance (8 km) illustrates that displacement is the straight-line distance from start to finish, while total distance includes all path segments regardless of direction.

## Practice Problem 2: Average Velocity and Acceleration

> A cyclist moves from $$x_0 = 5$$ m to $$x = 65$$ m in 12 s. Her velocity then changes from 4 m/s east to 10 m/s east in 3 s. Find (a) displacement, (b) average velocity for the 12 s interval, and (c) average acceleration for the 3 s interval.

**(a) Displacement:**

$$\Delta x = x - x_0 = 65 \text{ m} - 5 \text{ m} = 60 \text{ m east}$$

**(b) Average velocity:**

$$v_{avg} = \frac{\Delta x}{\Delta t} = \frac{60 \text{ m}}{12 \text{ s}} = 5.0 \text{ m/s east}$$

**(c) Average acceleration:**

$$a_{avg} = \frac{\Delta v}{\Delta t} = \frac{10 \text{ m/s} - 4 \text{ m/s}}{3 \text{ s}} = \frac{6 \text{ m/s}}{3 \text{ s}} = 2.0 \text{ m/s}^2 \text{ east}$$

## Practice Problem 3: Instantaneous Values

> A runner's average velocity from $$t = 2.0$$ s to $$t = 2.1$$ s is 6.2 m/s east, and from $$t = 2.0$$ s to $$t = 2.01$$ s is 6.0 m/s east. What do these values suggest about the runner's instantaneous velocity at $$t = 2.0$$ s?

Because the average velocity over very small time intervals is close to the instantaneous velocity, these values suggest the runner's instantaneous velocity at $$t = 2.0$$ s is about 6.0 m/s east. As we shrink the time interval closer and closer to zero, the average velocity gets closer to the true instantaneous value, and the trend here points toward approximately 6.0 m/s east.

## Common Misconceptions

- Distance and displacement are not the same. Distance is the total path length and is always positive, while displacement is a vector that can be positive, negative, or zero.
- A negative acceleration does not always mean slowing down. It means acceleration points in the negative direction. Whether the object speeds up or slows down depends on the direction of its velocity.
- Constant speed does not mean zero acceleration. If direction changes, the object is accelerating even though its speed stays the same.
- Average velocity is not the average of two speeds. It is total displacement divided by total time, which can give a different result.
- Instantaneous velocity is not just a smaller average. The average over a tiny interval approximates it, but the instantaneous value is the exact rate of change at one moment.

## Related AP Physics 1 Guides

- [1.1 Scalars and Vectors in One Dimension](/ap-physics-1-revised/unit-1/1-scalars-and-vectors-in-one-dimension/study-guide/4jyE1aiM5EBRDi9A)
- [1.3 Representing Motion](/ap-physics-1-revised/unit-1/3-representing-motion/study-guide/3s3qyB2ey6r2Q1UI)
- [1.4 Reference Frames and Relative Motion](/ap-physics-1-revised/unit-1/4-reference-frames-and-relative-motion/study-guide/iTcYEEULwbQlf2nW)
- [1.5 Vectors and Motion in Two Dimensions](/ap-physics-1-revised/unit-1/5-vectors-and-motion-in-two-dimensions/study-guide/LvdiAzU3amzMqu6O)

## Vocabulary

- **acceleration**: The rate of change of velocity with respect to time.
- **average acceleration**: The change in velocity of an object divided by the time interval over which that change occurs.
- **average velocity**: The displacement of an object divided by the time interval over which that displacement occurs.
- **displacement**: A vector quantity representing the change in position of an object from its initial to final location.
- **instantaneous acceleration**: The acceleration of an object at a specific instant in time, equal to the slope of the tangent line to a velocity-time graph.
- **instantaneous velocity**: The velocity of an object at a specific instant in time, equal to the slope of the tangent line to a position-time graph.
- **object model**: A simplification in physics where an object is treated as a single point with properties like mass and charge, ignoring size, shape, and internal structure.
- **position**: A vector quantity describing the location of an object relative to a reference point.
- **time interval**: The duration of time over which a change in an object's motion is measured.
- **velocity**: A vector quantity that describes both the speed and direction of an object's motion.

## FAQs

### What is displacement in AP Physics 1?

Displacement is the change in an object's position. In one dimension, use Delta x = x - x0, including the sign to show direction.

### What is the velocity formula for average velocity?

Average velocity is displacement divided by the time interval: v_avg = Delta x / Delta t. Because velocity is a vector, direction matters.

### What is average acceleration?

Average acceleration is the change in velocity divided by the time interval: a_avg = Delta v / Delta t.

### What is the difference between distance and displacement?

Distance is the total path length and is always positive. Displacement is the straight-line change in position and can be positive, negative, or zero.

### Can an object accelerate at constant speed?

Yes. An object accelerates if the magnitude or direction of velocity changes, so turning at constant speed still counts as acceleration.

### How are average and instantaneous velocity related?

Average velocity over a very small time interval gives a value close to instantaneous velocity at that moment.

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