83.4 Rectilinear motion with a constant acceleration 2. Rectilinear motion with a constant acceleration dy fr rom dt We have vx(r) dv (t) (t=v+a. dx(t) Likewise. from =v(t) dt We have dx(t) dt=L(vro +a t)dt x(o=xo+vrot+a,t 2 83.4 Rectilinear motion with a constant acceleration One-dimensional motion with constant acceleration a = constant where a=a v(t)=vro+a,t where v(t)=v,(t)i x(t)=xo+vrot+=,. where r(t=x(t)i Eliminate t in equations about v and x Vx m.(x一7 2. Rectilinear motion with a constant acceleration from x x a t v t = d d ( ) We have v t v a t v t a t x x x x v t v x x x = + = ∫ ∫ 0 t 0 ( ) ( ) d ( ) d 0 Likewise, from ( ) d d ( ) v t t x t = x We have 2 0 0 0 0 t 0 ( ) 2 1 ( ) d ( ) d ( )d 0 x t x v t a t x t v t v a t t x x t x x x x t x = + + = = + ∫ ∫ ∫ §3.4 Rectilinear motion with a constant acceleration One –dimensional motion with constant acceleration: v t v a t v t v t i x x x x ˆ ( ) where ( ) ( ) = 0 + = r x t x v t a t r t x t i x x ˆ where ( ) ( ) 2 1 ( ) 2 = 0 + 0 + = r a a a i x x where ˆ = constant =r §3.4 Rectilinear motion with a constant acceleration Eliminate t in equations about vx and x 2 ( ) 0 2 0 2 v x − v x = ax x − x