# Acceleration Calculation Exercises

## Description

This is a simple physics calculation tutorial aimed at high school students in grades 11 and 12 that runs through a couple of simple acceleration calculations: one each of positive acceleration, and negative acceleration. At the very bottom, you'll find a worksheet of exercises you can work through in your own time to consolidate your understanding. The video tutorial will be up shortly.

## Example 1

What acceleration does a car need in order to change its velocity from 3.0 m/s East to 6.5 m/s East in 5 seconds?

To tackle this calculation, let's list all of our variables:

• the initial velocity = 3.0 m/s East or + 3.0 m/s
• the final velocity = 6.5 m/s East or + 6.5 m/s
• the time in which this change occurred = 5 seconds

Now you just need to plug these variable into the equation, as shown below.

We know that the car has undergone positive acceleration because the sign of the calculated acceleration (+0.7 m/s2) is the same as the sign of the initial velocity (+3.0 m/s). The term positive acceleration implies that the acceleration has occurred in the same direction that the car was initially travelling in, but you can add "to the East" as a suffix to your answer above too.

## Example 2

What acceleration does a car need in order to change its velocity from 9.0 m/s South to 4.5 m/s South in 10 seconds? To tackle this calculation, let's list all of our variables again:

• the initial velocity = 9.0 m/s South or - 9.0 m/s
• the final velocity = 4.5 m/s South or - 4.5 m/s
• the time in which this change occurred = 10 seconds

Now you just need to plug these variables into the equation, as shown below.

We know that the car has undergone negative acceleration because the sign of the calculated acceleration (+0.5m/s2) is the opposite as the sign of the initial velocity (-9.0 m/s). Your final answer can either be that the car has undergone negative acceleration, or that it's accelerated at 0.5 m/s2 in the northerly direction (i.e. opposite to the direction it's travelling in).

## What if the direction changes?

It depends. When the direction changes within the same plane, you follow the calculations as above (there are some worked-through exercises in the below exercise worksheet). When the object changes direction in any way other than 180 degrees, then trigonometry is required to calculate the associated acceleration. That is beyond the scope of this basic tutorial, but will be covered in due course.

## Exercise Worksheet

This worksheet has six exercises that you can work through in your own time, with answers given in meters per second, kilometers per hour and miles per hour. To download the document visit Slideshare here: