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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

how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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what is energy?
James Reply
can anyone tell who founded equations of motion !?
Ztechy Reply
n=a+b/T² find the linear express
Donsmart Reply
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
Centre of mass of two uniform rods of same length but made of different materials and kept at L-shape meeting point is origin of coordinate
Rama Reply
A balloon is released from the ground which rises vertically up with acceleration 1.4m/sec^2.a ball is released from the balloon 20 second after the balloon has left the ground. The maximum height reached by the ball from the ground is
Lucky Reply
work done by frictional force formula
Sudeer Reply
Torque
Misthu Reply
Why are we takingspherical surface area in case of solid sphere
Saswat Reply
In all situatuons, what can I generalize?
Cart Reply
the body travels the distance of d=( 14+- 0.2)m in t=( 4.0 +- 0.3) s calculate it's velocity with error limit find Percentage error
Clinton Reply
Explain it ?Fy=?sN?mg=0?N=mg?s
Admire 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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