# Positive and Negative Acceleration

## Description

This is a simple physics tutorial aimed at high school students in grades 11 and 12 (IB, HSC) that runs through the concept of positive and negative acceleration and how it compares to 'acceleration and deceleration'. Video tutorial to come shortly.

## Introduction

In previous material (and in everyday language), we've learned that:

• Any increase in speed = acceleration
• Any decrease in speed = deceleration

Now we're going to move into more intricate definitions, and use the terms 'positive' and 'negative' acceleration.

### What is Positive Acceleration?

Positive acceleration refers to any object that is experiencing a force acting on it in the same direction it is travelling in. In this scenario, the object increases speed, but continues to travel in the same direction.

### What is Negative Acceleration?

Negative acceleration refers to any object that has a force acting on it in a direction that is opposite to what it is initially travelling in. In this scenario the object may:

• travel at a greater speed, but in the opposite direction, OR
• travel at a slower speed, in the opposite direction, OR
• travel at a slower speed and in the same direction (known as deceleration), OR
• have simply changed direction (to opposite direction) (but is travelling at the same speed).

## Determining positive and negative acceleration

### Step 1: Assign Signs

We can describe directions either with words (e.g. up/north or down/south) or with symbols (e.g. using the minus or plus symbols). Conventionally, we attribute positive signs to the north and east direction; and negative signs to the south and west.

### Step 2: Perform Calculation

Use this equation to calculate acceleration.

### Step 3: Determine if acceleration is positive or negative

Instinctively you'd think that if the calculated acceleration is positive, it means that the object is undergoing positive acceleration, and vice versa. This is not the case.

Instead, we need to compare the sign of the calculated acceleration with the sign of the initial velocity. What sign? I hear you ask. The sign that tells you what direction the initial velocity and the acceleration are in. Let's look at how we can define directions with signs.

• When an object is undergoing positive acceleration, the acceleration sign will be the same sign as the initial velocity.
• When an object is undergoing negative acceleration, the acceleration sign will be the opposite sign as the initial velocity.

If you're still not sure why we can't assume that the calculated acceleration sign is the same as the type of acceleration the object is undergoing, check out this tutorial.