Rectiliner Motion Study

7/30/2019 Rectiliner Motion Study

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MotionWhen we observe our surroundings, we can see many physical interactions taking placearound us like a book falling, an ear drum vibrating, bus moving, nuclear reactions etc. If

we want to express these interactions in terms of physics, we call it asmotion .If an object is moving, we would be curious to know what are the things happening thatmake a body move, how long will a body move and many other things.To understand that we will study the topic of motion.

A motion diagram for an object whose acceleration points opposite the velocity, themagnitude of the velocity decreases as these progress.

The following are the terms that should be studied before dealing with motion :

Rest : When the body does not change its position with respect to the surroundings, thebody is said to be at rest.

Example: A person, sitting inside a moving bus, is at rest with respect to the personsitting next to him as he is not changing his position.

Motion: When the body changes its position with respect to the surroundings, the body issaid to be in motion.

Example: Considering Sun as reference point, planets change its position, so, planets arein motion.

Motion and Rest are relative terms, for example, the person, sitting inside the movingtrain, is at rest to the person sitting next to him but he is in motion with respect to theperson outside the moving train.Similarly, on Earth, we are in rest with respect to each other but we are in motion withrespect to the Sun.


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What is Motion? Back to Top

When the body changes its position with respect to its surrounding, the body is said to bein Motion.

Examples: Football on ground, motion of moon around earth, person inside a movingbus with respect to person outside the bus, bird flying in sky are the examples of motion.

Distance and Displacement Back to Top

The minimum distance between two points is calleddisplacement while the actual pathcovered is calleddistance . The displacement is a vector term and distance is scalar term.Distance and displacement both have SI unit as meter.

AB + BC = distance moved and AC = displacement

The effect of AB + BC is same as effect of AC.

On one round trip, distance is 2(AB + BC) while the displacement = AC + CA = 0Hence the distance is never zero while the displacement is zero in one round trip.As we know that the rate of change of displacement is velocity similarly we have,Speed = Distance movedTime taken S =dt where d is distance moved.The SI unit for velocity and speed is meter/second (m/s).The speed is scalar term and velocity isvector term.The speed cannot be zero since distance cannot be zero while the velocity can be zero asdisplacement can be zero. Read More

Types of Motion Back to Top

The types of motion are:


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Uniform motion Non uniform motion

a) Uniform motion: When equal distance is covered in equal interval of time, the motionis said to be in uniform motion.

The bodies moving withconstant speedor velocity have uniform motion or increase atthe uniform rate.

b) Non Uniform motion: When unequal distances are covered in equal interval of time,the motion is said to be in non uniform motion. The bodies executing non uniform motionhave varying speed or velocity.

We can even classify motion into three types:

Translatory motion Rotatory motion

Vibratory motion

Translatory MotionIn translatory motion the particle moves from one point in space to another. This motionmay be along a straight line or along a curved path.They can be classified as:

1. Rectilinear Motion Motion along a straight line is called rectilinear motion.

2. Curvilinear Motion Motion along a curved path is called curvilinear motion.

Rotatory Motion

In Rotatory motion, the particles of the body describe concentric circles about the axis of motion.

Vibratory Motion

In Vibratory motion the particles move to and fro about a fixed point.Equations of Motion Back to Top

The variable quantities in a uniformly accelerated rectilinear motion are time, speed,distance covered and acceleration. Simple relations exist between these quantities. These


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relations are expressed in terms of equations called equations of motionThere are three equation of motion.

1) v = u+at2) S = ut + 12 at 2

3) v2

= u2

+ 2as. Where v = Final Velocityu = Initial velocitya = accelerations = distance traveled by a bodyand t = time taken.

Derivation of Equation of Motion

First Equation of Motion:

Consider a particle moving along a straight line with uniform acceleration 'a'. At t=0, letthe particle be at A and u be its initial velocity and when t=t, V be its final velocity.

Acceleration = Change In Velocity / TimeAcceleration =change i n velocity/Time = vu /t .at = v-uv = u+ at ........ First equation of motion.

Second Equation of Motion:Average Velocity = Total Distance Travelled / Total Time taken

= s / t ---------------(1)Also Average Velocity = (u + V) / 2 ----------(2)

Equate 1 & 2----we gets/t = (u + v)/2------------(3)s = (2u+at )t 2 = 2ut +at 22 = 2ut 2 + at 22 Second equation of motion.Third equation of Motion The first equation of motion is v = u + at.

v - u = at ... (1)

Average velocity =st ... (2)


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Average velocity =u+v2 ... (3)From equation (2) and equation (3) we get,

u+v2 = st ... (4)

Multiplying eq (1) and eq (4) we get,

(v - u)(v + u) = at x2st

(v - u)(v + u) = 2as

[We make use of the identity a2 - b2 = (a + b) (a - b)]v2 - u 2 = 2as.......................... Third equation of motion.

Derivation of Equation of Motion(Graphically)

First Equation of Motion

Consider an object moving with a uniform velocity u in a straight line. Let it be, given auniform acceleration at time, t = 0 when its initial velocity is u. As a result of theacceleration, its velocity increases to v (final velocity) in time t and s is the distancecovered by the object in time t. The figure shows the velocity-time graph of the motion of the object.

Slope of the v - t graph gives the acceleration of the moving object.Thus, acceleration = slope = AB = BCAC = vut 0 a =vut

v - u = at

v = u + at................................................................(1)


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Let u be the initial velocity of an object and 'a' the acceleration produced in the body. Thedistance traveled s in time t is given by the area enclosed by the velocity-time graph forthe time interval 0 to t.

Distance traveled s = area of the trapezium ABDO

= area of rectangle ACDO + area of ABC

= OD x OA +1/2BC x AC

= t x u +1/2 (v - u) x t

= ut +1/2 (v - u) x t

(v = u + at I eqn of motion; v - u = at)S = ut +1/2at x t

S = ut + 12at 2

Third Equation of MotionLet 'u' be the initial velocity of an object and a be the acceleration produced in the body.The distance travelled 's' in time 't' is given by the area enclosed by the v - t graph.


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a) For body moving at constant velocity:

The graph of straight line parallel to the X axis shows that the body is moving withconstant velocity.

b) For uniform motion:

This graph shows the equal displacement in equal interval of time so, theslope = Y / X gives the change in position over corresponding change in time isconstant. Thus, this graph shows the uniform motion.

c) For Body at Rest:

The position-time graph parallel to time axis shows that the body is at rest.d) For Non uniform motion:

This graph shows unequal distance in equalinterval of time which gives the change in position over corresponding change in timewhich is varying.

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Rectiliner Motion Study