# 0.2 Motion in one dimension  (Page 14/16)

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## Graphs

1. A car is parked $10\phantom{\rule{2pt}{0ex}}\mathrm{m}$ from home for 10 minutes. Draw a displacement-time, velocity-time and acceleration-time graphs for the motion. Label all the axes.
2. A bus travels at a constant velocity of $12\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ for 6 seconds. Draw the displacement-time, velocity-time and acceleration-time graph for the motion. Label all the axes.
3. An athlete runs with a constant acceleration of $1\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-2}$ for $4\phantom{\rule{2pt}{0ex}}\mathrm{s}$ . Draw the acceleration-time, velocity-time and displacement time graphs for the motion. Accurate values are only needed for the acceleration-time and velocity-time graphs.
4. The following velocity-time graph describes the motion of a car. Draw the displacement-time graph and the acceleration-time graph and explain the motion of the car according to the three graphs.
5. The following velocity-time graph describes the motion of a truck. Draw the displacement-time graph and the acceleration-time graph and explain the motion of the truck according to the three graphs.

This simulation allows you the opportunity to plot graphs of motion and to see how the graphs of motion change when you move the man.

run demo

## Equations of motion

In this chapter we will look at the third way to describe motion. We have looked at describing motion in terms of graphs and words. In this section we examine equations that can be used to describe motion.

This section is about solving problems relating to uniformly accelerated motion. In other words, motion at constant acceleration.

The following are the variables that will be used in this section:

$\begin{array}{ccc}\hfill {v}_{i}& =& \mathrm{initial velocity}\phantom{\rule{2pt}{0ex}}\left(\mathrm{m}·{\mathrm{s}}^{-1}\right)\phantom{\rule{2pt}{0ex}}\mathrm{at}\phantom{\rule{2pt}{0ex}}\mathrm{t}=0\mathrm{s}\hfill \\ \hfill {v}_{f}& =& \mathrm{final velocity}\phantom{\rule{2pt}{0ex}}\phantom{\rule{2pt}{0ex}}\left(\mathrm{m}·{\mathrm{s}}^{-1}\right)\phantom{\rule{2pt}{0ex}}\mathrm{at time}\phantom{\rule{2pt}{0ex}}\mathrm{t}\hfill \\ \hfill \Delta x& =& \mathrm{displacement}\left(\mathrm{m}\right)\hfill \\ \hfill t& =& \mathrm{time}\left(\mathrm{s}\right)\hfill \\ \hfill \Delta t& =& \mathrm{time interval}\phantom{\rule{2pt}{0ex}}\left(\mathrm{s}\right)\hfill \\ \hfill a& =& \mathrm{acceleration}\left(\mathrm{m}·{\mathrm{s}}^{-1}\right)\hfill \end{array}$
$\hfill {v}_{f}& =& {v}_{i}+at\hfill$
$\hfill \Delta x& =& \frac{\left({v}_{i}+{v}_{f}\right)}{2}t\hfill$
$\hfill \Delta x& =& {v}_{i}t+\frac{1}{2}a{t}^{2}\hfill$
$\hfill {v}_{f}^{2}& =& {v}_{i}^{2}+2a\Delta x\hfill$

The questions can vary a lot, but the following method for answering them will always work. Use this when attempting a question that involves motion with constant acceleration. You need any three known quantities ( ${v}_{i}$ , ${v}_{f}$ , $\Delta x$ , $t$ or $a$ ) to be able to calculate the fourth one.

1. Read the question carefully to identify the quantities that are given. Write them down.
2. Identify the equation to use. Write it down!!!
3. Ensure that all the values are in the correct unit and fill them in your equation.
4. Calculate the answer and fill in its unit.

## Interesting fact

Galileo Galilei of Pisa, Italy, was the first to determined the correct mathematical law foracceleration: the total distance covered, starting from rest, is proportional to the square of the time. He also concluded thatobjects retain their velocity unless a force – often friction – acts upon them, refuting the accepted Aristotelian hypothesis thatobjects "naturally" slow down and stop unless a force acts upon them. This principle was incorporated into Newton's laws of motion(1st law).

## Finding the equations of motion

The following does not form part of the syllabus and can be considered additional information.

According to the definition of acceleration:

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