# 1.17 Understanding motion

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Our success or failure in understanding motion largely depends on our ability to identify motion according to a certain scheme of classification.

The discussion of different attributes of motion in previous modules has led us to the study of motion from the point of view of a general consideration to a simplified consideration such as uniform or rectilinear motion. The time is now ripe to recapitulate and highlight important results - particularly where distinctions are to be made.

For convenience, we shall refer general motion as the one that involves non-linear, two/ three dimensional motion. The simplified motion, on the other hand, shall refer motion that involves one dimensional, rectilinear and uniform motion.

Consideration of scalar quantities like distance and speed are same for “general” as well as “simplified” cases. We need to score similarities or differences for vector quantities to complete our understanding up to this point. It is relevant here to point out that most of these aspects have already been dealt in detail in previous modules. As such, we shall limit our discussion on main points/ results and shall generally not use figures and details.

## Similarities and differences

Similarity / Difference 1 : In general, the magnitude of displacement is not equal to distance.

$\begin{array}{l}|\Delta \mathbf{r}|\le s\end{array}$

For rectilinear motion (one dimensional case) also, displacement is not equal to distance as motion may involve reversal of direction along a line.

$\begin{array}{l}|\Delta x|\le s\end{array}$

For uniform motion (unidirectional motion),

$\begin{array}{l}|\Delta x|=s\end{array}$

Similarity / Difference 2 : The change in the magnitude of position vector is not equal to the magnitude of change in position vector except for uniform motion i.e motion with constant velocity.

For two/three dimensional motion,

$\begin{array}{l}\Delta r\ne |\Delta \mathbf{r}|\end{array}$

For one dimensional motion,

$\begin{array}{l}\Delta x\ne |\Delta x|\end{array}$

For uniform motion (unidirectional),

$\begin{array}{l}\Delta x=|\Delta x|\end{array}$

Similarity / Difference 3 : In all cases, we can draw a distance – time or speed – time plot. The area under speed – time plot equals distance (s).

$\begin{array}{l}s=\int vdt\end{array}$

Similarity / Difference 4 : There is an ordered sequence of differentiation with respect to time that gives motional attributes of higher order. For example first differentiation of position vector or displacement yields velocity. We shall come to know subsequently that differentiation of velocity, in turn, with respect to time yields acceleration. Differentiation, therefore, is a tool to get values for higher order attributes.

These differentiations are defining relations for the attributes of motion and hence applicable in all cases irrespective of the dimensions of motion or nature of velocity (constant or variable).

For two or three dimensional motion,

$\begin{array}{l}\mathbf{v}=\frac{d\mathbf{r}}{dt}\end{array}$

For one dimensional motion,

$\begin{array}{l}v=\frac{dx}{dt}\end{array}$

Similarity / Difference 5 : Just like differentiation, there is an ordered sequence of integration that gives motional attributes of lower attributes. Since these integrations are based on basic/ defining differential equations, the integration is applicable in all cases irrespective of the dimensions of motion or nature of velocity (constant or variable).

#### Questions & Answers

How can we take advantage of our knowledge about motion?
Kenneth Reply
pls explain what is dimension of 1in length and -1 in time ,what's is there difference between them
Mercy Reply
what are scalars
Abdhool Reply
show that 1w= 10^7ergs^-1
Lawrence Reply
what's lamin's theorems and it's mathematics representative
Yusuf Reply
if the wavelength is double,what is the frequency of the wave
Ekanem Reply
What are the system of units
Jonah Reply
A stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight, calculate the angle of projection, calculate the range attained
Samson Reply
58asagravitasnal firce
Amar
water boil at 100 and why
isaac Reply
what is upper limit of speed
Riya Reply
what temperature is 0 k
Riya
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
Mustapha
How MKS system is the subset of SI system?
Clash Reply
which colour has the shortest wavelength in the white light spectrum
Mustapha Reply
how do we add
Jennifer Reply
if x=a-b, a=5.8cm b=3.22 cm find percentage error in x
Abhyanshu Reply
x=5.8-3.22 x=2.58
sajjad
what is the definition of resolution of forces
Atinuke Reply

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 By Yasser Ibrahim By Jonathan Long By Jonathan Long By Stephen Voron By Jesenia Wofford By Laurence Bailen By Richley Crapo By Madison Christian By Vanessa Soledad By OpenStax