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 dtdt4 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