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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.

| Δ r | s

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

| Δ x | s

For uniform motion (unidirectional motion),

| Δ x | = s

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,

Δ r | Δ r |

For one dimensional motion,

Δ x | Δ x |

For uniform motion (unidirectional),

Δ x = | Δ x |

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).

s = v t

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,

v = r t

For one dimensional motion,

v = x t

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

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
what is energy?
James Reply
Ability of doing work is called energy energy neither be create nor destryoed but change in one form to an other form
Abdul
motion
Mustapha
highlights of atomic physics
Benjamin
can anyone tell who founded equations of motion !?
Ztechy Reply
n=a+b/T² find the linear express
Donsmart Reply
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عباس
Quiklyyy
Sultan Reply
Moment of inertia of a bar in terms of perpendicular axis theorem
Sultan Reply
How should i know when to add/subtract the velocities and when to use the Pythagoras theorem?
Yara Reply

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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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