84.1 The position, velocity and acceleration vectors in two dimensions v(t=lim r(+△)-r(t)dr( M→0s c. The components of the velocity in Cartesian coordinate system dr(t) dx(t):, dj A v(t) =v,(t)i+v,(t) dt d dt Magnitude:y=/(6)=[v2(0)+22(0v ds+ dt Direction: tangent to the path followed by the particle; or 0= tan-y The angle between v and x-axis 84.1 The position velocity, and acceleration vectors in two dimensions v(t) rajectory t+△n v(t+At v(t+At) 4. Acceleration vector Average acceleration Av(0 v(t+4r)-v( t3 t r t t r t t r t v t t d ( ) ( ) d ( ) ( ) lim 0s r r r r = ∆ + ∆ − = ∆ → c. The components of the velocity in Cartesian coordinate system j v t i v t j t y t i t x t t r t v t x y ˆ ( ) ˆ ( ) ˆ d d ( ) d d ( ) d d ( ) ( ) = = + = + r r r §4.1 The position, velocity, and acceleration vectors in two dimensions Magnitude: t s v v t v t v t x y d d ( ) [ ( ) ( )] 2 2 1 2 = = + = r Direction: tangent to the path followed by the particle; or x y v v 1 tan− θ = The angle between v and x − axis r §4.1 The position, velocity, and acceleration vectors in two dimensions 4. Acceleration vector a. Average acceleration v(t) r v(t + ∆t) r v(t) r ∆ t v t t v t t v t a ∆ ∆ ∆ ∆ ( ) ( ) ( ) ave r r r r + − = = x y O v(t) r v(t + ∆t) r