4.1 The position, velocity, and acceleration vectors in two dimensions 2. The path(trajectory) of a particle x=x(t) y=y(t) Eliminating y=y(x) Example 1: r(t)=A cos ati+ B sin atj x=x(t=Acos @t V= y(t)=b sin at 十 A2B 84.1 The position velocity, and acceleration vectors in two dimensions 3. Speed and velocity vector a Average speed and instantaneous speed As ave ∠t as d v= m →0 4t dt b Average velocity and instantaneous velocity m布r(t+A)-F(t) Notes≠ ∠t Ive2 2. The path (trajectory) of a particle ( ) ( ) y y t x x t = = Eliminating t y = y(x) Example 1: 1 ( ) sin ( ) cos ˆ sin ˆ ( ) cos 2 2 2 2 + = = = = = = + B y A x y y t B t x x t A t r t A ti B tj ω ω ω ω r §4.1 The position, velocity, and acceleration vectors in two dimensions §4.1 The position, velocity, and acceleration vectors in two dimensions 3. Speed and velocity vector a. Average speed and instantaneous speed t s t s v t s v t d d lim 0s ave = = = → ∆ ∆ ∆ ∆ ∆ b. Average velocity and instantaneous velocity t r t t r t t r v ∆ ∆ ∆ ∆ ( ) ( ) ave r r r r + − = = x y O ∆s Note: ave ave v v r ≠