# 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.

## Derivation of [link]

According to the definition of acceleration:

#### Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
how did you get the value of 2000N.What calculations are needed to arrive at it
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