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So SEE fl, , , , , , , , isplacement, velocity,, » acceleration andtime of a given motion, without ne the forces that cause the, motion., Kinetics deals with the relationship between the motion of bodies and forces acting on |:, , imension (rectilinear mo ion): “The inotion along a straight line is, known as rectilinear motion. The important parameters required to study the motion, along a straight line are position, displacement, velocity, and acceleration., , Position, displacement and distanct' travelled by the particle: The motion of a, _Particle can be described if its “Known continuously with respect to time., The total length of the puth is the distance'traveiled by the particle and the shortest |, , Tet, , eLEL:, , =, , , , , , , , distance travelled ‘by a particle, however, is different from its displacement from the, origin. For example, if the particle moves from a point O to position P, and then to, position P, its displacement at the position P2 is — x2 from the origin but, the distance, travelled by the particle is x;+x1+x2 = (2x1+x2) (Fig)., , The distance travelled is a scalar quantity and the displacement is a vector quantity., , % &, er § ~, , Ke —_$_ 1 1 — > 7X, », 0 B,, , Distance and displacement, , , , , , , , , , , , , , saad, Speed: It is s the distance travelled in unit time, Itisa scalar quantity., , , , Ans:, , the particle, It is also defined as the speed of the particle in a given direction. The, velocity is a vector quantity. It has both magnitude and direction., , STE, , , , , * distance between the initial and final ‘position of the particle is the displacement. The |}\, , , , Velocity: The velocity of a particle is defined as the rate of change of displacernent of |, , , , , , , , , , , , , , iy, Ad Le, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Velocity = displacement/time taken ;, Its unit is ms“! and its dimensional formula is LT., , , , , , , , , , te: @rediffmail com |, , , , er, I @ Sanguine! Multimedia Studies: www. smsinotes.pag, , , , Scanned with CamScanner
Page 2 : raw its position time. graph?, , , , , , ; cit if it moves alone, i Ans: Uniform velocity: A particle is said to move with st y, ig, i a fixed direction and covers equal displacements i = : fea, ne intervals of time, however small these intecvall of time may, é “ tarit at, is Ina displacement - time stag (Fig.) the — is cons _ |, 3, all the points, when the particle moves with uniform velocity., , , , ity. is‘variable™ (non-tmniforn}), if it, , “Non uniformor: variable: velovity:. ‘The veloeit, f time. or. if the direction of motion_, , covers unequal displacements in equal i in, , te ~ changes or if both-the rate of motion-and.t, , , , , , , , , , Sanu, , , , , , , , , , , , ==, , , , , , , , , , as, , ine Movement of an object along a straight line, , , , Movement of a body along a straig], , | with steady speed. with variable speed., tat Covers equal distances in equal time Covers unequal distances in equal time, =I interval. \ interval., , Average speed is similar to actual.s etl; Average speed is different from actual speed, , - of the object. ‘Ofthe object., Distance-time graph shows a straight | tine. Distance-time graph shows a curved line., ue Rectilinear motion has non-zero,, Recillingar motion has zero acceleration. acceleration., , , , Einiied, , , , ae ae, , , , , , , , , , , , , , , , , , , , , , , Define‘average and instantaneous velocity?’ - :, , Average velocity: Let s; be the displacement of a body in time ty ‘and $2 be i its, , displacement in time f2 (Fig.)., , The average velocity during the time interval (f2— 7) is. 5, , defined as, , change in displacement, change in time, , , , Vaverage =, , nye, , ROHL, , , , , , 2, , From the graph, it is found that the slope of the curve varies. . : : g, Instantaneous velocity: It is the velocity at any given instant of time or at any given ei, point of its path. The instantaneous velocity v is given by i, , As _ ds, , ‘Lt, ~ Ato “AL dt, , Sangdre=Multimedia-Stittes, , , , , , , , , , , , , , , , , , www.smsinotes,paged. mé
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Strares, , , , , , , , ines, , SEU eStats, , , , , - Ans: Acceleration: If the magnitude or the direct, , , , , , , , , , , , , , , , , , , , , , , , , , , , y (Instant WVotes|, , , , , , , , , , “Define acceleratio: ee, ion or both of the velocity changes with, respect to time, the particle is said to be under acceleration., , Acceleration of a particle is defined as the rate of change of velocity. Acceleration is a, vector quantity, ,, , Change in velocity, ~~ time taken - M r, , .._I£u.is the. initial velocity_and vy, the final velocity of the. particle after.a time, then the, ——acceleration——— : =, . -- 4, , Vaz, a=, t, Its unit is m s™ and its dimensional formula is LT™,, , .. Acceleration =, , , , \, , , ad dv_d(ds\ @, The instantaneous acceleration is,a= Ye $(#) = ear, It, , dt dt\ dt, form acceleration?’ : e, Uniform acceleration: If the velocity changes by an equal amount in equal interva, , of time, however smail these intervals of time may be, the acceleration is said to be, 1%, uniform. ., , , , , , , , , , , , , , , , , , , , , , , , Discuss velocity time graph?, Velocity — time graph: When the, time, it is velocity-time graph., , Ans: yelocity-of the particle is plotted as a function of 1, , As 4= *. the slope of the v — 7 curve at any instant gives the acceleration of the, i :, particle (Fig.)., , , , : :, But, v= oS. or ds= y.dt, at, If the displacements are s; and s2 in times ty and t, °¢, then ‘, ‘jose fo ae, , 4 't, , , , =, 5,~ 5, = [vdt= area ABCD, a, , The area under the v — ¢ curve, between the given, intervals of time, gives the change in displacement, or the distance travelled by the particle during the °, same interval, ~, , , , , , , , , , 4, , i © Sanguine Multimedia Studies: www.sms1notes.page4.me e smsinotes rediffmail.com es, , , , Scanned with CamScanner
Page 4 : \, , , , , , , , , , , , , , CUSS Position:, Position - Time graphs, with respect to time,, For Example,, , X (position), , , , Savi, , , , , , , , iD fies, , , , , , , , MELE SU, , THIEN:, , STE, , SSS, , Sti, , , , , , =, , , , mesic, , Tine, , &, , TL, , , , , , , , , , Sane, , , , , , Gihnies, , , , , , , , , , , , , , , , , , , , , , , , , , , , Sin, , , , Sang!, , t(time) \ iC, , Above position — time graph Tepresents an object at rest at position x), in positive direction., X (position), , , , _ t (time), , Above position — time graph represents particle, until, t = ty, it stops moving. Finally,, velocity, v), in opposite direction., Position — Time graphs are also called x - t graphs., , Slope cf Position — Time graph gives instamaneous velocity., , + — Slope of any curve = dy/dx(Revisit Differential Calculus for more details), + Slope of position-time graph = di/dt = inst.velocity ,, , WERE ATE, , going at uniform velocity in positive direction f, it changes direction and starts moving’ with uniform, , , , , , , , , , , , uss graphically uniformly accelerated moti 3 : 4, The distance-time graph for a uniformiy accelerated motion looks as shown in the |, graph, consider how the distance is changing exponentially indicating that the velocity,, is changing at a constant rate or there is constant acceleration. But in the velocity time.", graph as velocity changes at a constant rate with Tespect to time in uniformly, accelerating motion, the graph wouid be a straight line\with its slope indicating the, , amount of acceleration., , _—_—__—_+, , , , , , distance, , velocity, , , , , , , , , , , , , , , , time, jest Www.smsinotes.page4.me
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Scalar Quantity: The term seal quantity’ is defined as a cquaniiy that has only one, element of a number field, attached to a unit of measurements, such as degrees or, meters. It is a quantity that exhibits magnitude or size only, i.e. it is defined by a, numerical value, along with a measurement unit. For example, Speed of the car, body, temperature, distance between two locations, etc. . i, , “ete Vector Quantity:A’ mathématical quantity that needs two independent’ characteristics, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , y, , to describe it completely, i.c. magnitude and direction. Here magnitud represents the |!, , —“size-of the quantity which is_also-jts- -absolute-value,-while_direction_represents-the |:, , 2 side, i.e. east, west, north, south, etc, For example, Displacement between two points, Ki, , ie velocity and acceleration of a moving body, force, weight, etc, EI f, , ny physical quantity that Vector quantity is one, that has |, , Ly does not include direction is. . both magnitude and direction. ie, , |" known as scalar quantity. . Bi, , iF Quantities One-dimensional quantities Multi-dimensional quantities Ey, , B iat - Change It changes with the change in _It changes with the change in’ SI, ft \- their magnitude. ne direction or magnitude or _, , Row 4 “f . 0 =, , Operations, .’ Follow ordinary rules of Follow rules of vector algebra. : ‘|, , . algebra. re, , , , , , Comparison of — Simple Complex By, two quantities fe oe z ep, Division Scalar can divide another Two vectors can never divide. al, , a, , , , , , , , , , , , , , , , acne victors a, ‘sition vector is used to. specify the position of a certain body., Knowing the position of a body is vital when it comes .to describe the motion of that, , , , , , , , , , , , “body. The position vector of an object is measured from the origin, in general. \%, Suppose an object is placed in the space as shown: Ei, Position vector (‘r)=xity*j+zk ie, Where, Lest 4, ‘i= unit vector along x direction __- oo !, , ‘j= unit vector along y direction, , “k= unit vector along z direction, , So if an object is at a certain point P (say) at a certain time,, its position vector is given as described above., , , , , , , , , , Oforigin), , , , , , , , , , , , Displacement Vector: The change in the position vector of an object is known as, displacement vector. Suppose an object is at point A at time = 0 and at point B at time, =t. The position vectors of the object at point A and at point B are given as:, Position vector at point A=PA=51+3j+4k, , i, , , , , , , , , , , , , , , , , , , ST Sa Pea, , , , I @ Sanguine Multimedia Studle: vowwi smisinotes. paged, me: msinotes@redifimail. com ae i, , Denne Bara ac, , , , Scanned with CamScanner
