84.1 The position, velocity and acceleration vectors in two dimensions b. Instantaneous acceleration (t)=li Av(t dv(t a→0st dt 4v() dv,()a dv, (t 十 dt v(t+4) =a(t)i+a,(t)j Magnitude: a=a(D)=[a2()+a2(0/2 , Direction: 6=tan The angle between a and x-axis 84.1 The position, velocity, and acceleration vectors in two dimensions C. The direction of acceleration: 4v=v-v vI> B B < g4 §4.1 The position, velocity, and acceleration vectors in two dimensions a t i a t j j t v t i t v t t v t t v t a t x y x y t ˆ ( ) ˆ ( ) ˆ d d ( ) ˆ d d ( ) d ( ) d ( ) ( ) lim 0s = + = + = = → r r r ∆ ∆ ∆ b. Instantaneous acceleration Magnitude: 2 2 1 2 a a(t) [a (t) a (t)] x y = = + r Direction: x y a a1 tan− θ = The angle between a and x − axis r v(t) r v(t + ∆t) r v(t) r ∆ c. The direction of acceleration： B A v v v r v r ∆ = − B A v v r r > A v r v r ∆ a α r g r v r A v r B v r B A v v r r < B v r v r ∆ a r g r α v r A v r B A v v r r = B v r v r ∆ a r α v r a r A v r B v r §4.1 The position, velocity, and acceleration vectors in two dimensions