UNIVERSITY PHYSICS I CHAPTER 3 Kinematics i Rectilinear motion Chapter 3 Kinematics i: rectilinear motion Motion implies change, and it is change make life-and physics-visible and interesting. Kinematics is the theory about the description of motion Physical theories are creations of the human intellect; they must be invented rather than discovered
1 Chapter 3 Kinematics I: rectilinear motion Kinematics is the theory about the description of motion. Physical theories are creations of the human intellect; they must be invented rather than discovered. Motion implies change, and it is change make life-and physics-visible and interesting
83.1 Position and displacement of a particle 1. Several concepts Frame of reference -any object that is chosen for reference of a motion Coordinate system-the abstract of reference Particle-a single mass point without shape. + An object whose part are all move in exactly the same way can be treated as a particle; or a complex object can be treated as a particle if there are no internal motions or the internal motions can be neglected for the problem which you are discussing 83.1 Position and displacement of a particle 2. The position vector and displacement vector of a particle in rectilinear motion Hi=il Displacement--the change of the position vector A=r-1=(x s-Ci)i=4xi Note: The magnitude of the displacement is not necessarily equal to the total distance as traveled by the particle during the time interval At. when Ar=0. As may be not zero
2 §3.1 Position and displacement of a particle 1. Several concepts Frame of reference —any object that is chosen for reference of a motion. Particle—a single mass point without shape. An object whose part are all move in exactly the same way can be treated as a particle; or a complex object can be treated as a particle if there are no internal motions or the internal motions can be neglected for the problem which you are discussing. Coordinate system—the abstract of reference 2. The position vector and displacement vector of a particle in rectilinear motion x O r x i i i ˆ = r x O r x i f f ˆ = r Note: r r r x x i xi f i f i ˆ ˆ ∆ = − = ( − ) = ∆ r r r Displacement—the change of the position vector §3.1 Position and displacement of a particle 1 The magnitude of the displacement is not necessarily equal to the total distance traveled by the particle during the time interval ∆t .when ∆r = 0 , ∆s may be not zero. r ∆s
83.1 Position and displacement of a particle Note Ar is independent of thethe specifi coordinate system we choose 3 The position of a moving particle is a function of time r(t)=x(t)i □■■■ ④ the path of the particle is a straight line t A graph ofx versus t 83.2 The speed and velocity of a moving particle 1. Average speed and average velocity Ar Define: aveRt ave t 个:d≠EF v≠v 2. Instantaneous velocity H and instantaneous speed (t)=x(t) x(2 x(o r(t+A)=x(t+∠)i
3 Note: 3 The position of a moving particle is a function of time, r r 2 ∆ is independent of the the specific coordinate system we choose. r t x t i ˆ ( ) = ( ) r x t A graph of x versus t §3.1 Position and displacement of a particle 4the path of the particle is a straight line. 2. Instantaneous velocity and instantaneous speed §3.2 The speed and velocity of a moving particle 1. Average speed and average velocity Define: t s v ∆ ∆ ave = t r v ∆ ∆ r r ave = ave ave s r v v r r Q∆ ≠ ∆ ∴ ≠ t x 1 ∆t 2 ∆t x(t) ( )1 x t ( ) 2 x t r r t x t i i ˆ = ( ) = ( ) r r r r t t x t t i f ˆ = ( +∆ ) = ( +∆ ) r r
83.2 The speed and velocity of a moving particle Ar=r(t+At)r(t=x(t+At)-x(tli [x(t+)-x() ∠Lt Instantaneous velocity r(t+4)-r(t) dr v(t)=lim vave lim 一=—l dr→0s r→0s ∠t he component of the velocity: D (t=c T dt 83.2 The speed and velocity of a moving particle The direction of the velocity dx(t) dx(t) 0 same as dr <o opposite of Instantaneous speed v(t)=lim v lim As ds(t) dr→0s ave 4→0stdt ∵limr|=dr=d d→0s Ar dr d 40e/b lim lim ave r→0s At dtdt
4 r r t t r t x t t x t i ˆ ∆ = ( + ∆ ) − ( ) = [ ( + ∆ ) − ( )] r r r t x t t x t i t r v ∆ ∆ ∆ ∆ ˆ [ ( ) ( )] ave + − = = r r i t x t r t r t t r t v t v t t ˆ d d d ( ) ( ) d ( ) lim lim 0s ave 0s = = + − = = → → r r r r r ∆ ∆ ∆ ∆ Instantaneous velocity: The component of the velocity: t x t v t x d d ( ) ( ) = §3.2 The speed and velocity of a moving particle v t s t r t r v r r s t t t ∴ = = = = = = → → → d d d d lim lim lim d d 0s ave 0s 0s r r r r r Q ∆ ∆ ∆ ∆ ∆ ∆ Instantaneous speed: t s t t s v t v t t d d ( ) ( ) lim lim 0s ave 0s = = = → → ∆ ∆ ∆ ∆ The direction of the velocity: 0 d d ( ) > t x t 0 d d ( ) < t x t same as , i ˆ i opposite of ˆ §3.2 The speed and velocity of a moving particle
83.3 The acceleration in rectilinear motion 1.Average acceleration Define:ave== ave rave ∠t 2. Instantaneous acceleration if v;=v,(ti,v=v,(t+4t) Av=v-v,=lv(t+45)-v(x)i 83.3 The acceleration in rectilinear motion then as lim 4v= lim /(t+4t)-v2()i_dv() 4→0sAt→+0s dt or(= dv(t) dv(t): dr(t) d'x(t dt The instantaneous acceleration of a particle is the time rate of change of the velocity vector or the first derivative of the instantaneous velocity vector with respect to time; or the second derivative of the instantaneous position vector with respect to time
5 §3.3 The acceleration in rectilinear motion Define: t v v t v a f i ∆ ∆ ∆ r r r r − ave = = 1. Average acceleration i t v t v t a a i x f x i x ˆ ( ) ( ) ˆ ave ave ∆ − = = r 2. Instantaneous acceleration if v v v v t t v x i v v t i v v t t i f i x x i x f x ˆ [ ( ) ( )] ˆ , ( ) ˆ ( ) = − = + − = = + ∆ ∆ ∆ r r r r r then t v t t v t t v t i t v a x x t t d d ( ) ˆ [ ( ) ( )] lim lim 0s 0s r r r = + − = = → → ∆ ∆ ∆ ∆ ∆ ∆ or i t x t t r t i t v t t v t a x ˆ d d ( ) d d ( ) d d ( ) d d ( ) 2 2 2 2 = = = = r r r r The instantaneous acceleration of a particle is the time rate of change of the velocity vector or the first derivative of the instantaneous velocity vector with respect to time;or the second derivative of the instantaneous position vector with respect to time. §3.3 The acceleration in rectilinear motion