v = a t + v 0 [ 1 ] r = r 0 + v 0 t + 1 2 a t 2 [ 2 ] r = r 0 + 1 2 ( v + v 0 ) t [ 3 ] v 2 = v 0 2 + 2 a ⋅ ⋅ ( r − − r 0 ) [ 4 ] r = r 0 + v t − − 1 2 a t 2 [ 5 ] although the Torricelli equation [4] can be derived using the distributive property of the dot product as follows: v 2 = v ⋅ ⋅ v = ( v 0 + a t ) ⋅ ⋅ ( v 0 + a t ) = v 0 2 + 2 t ( a ⋅ ⋅ v 0 ) + a 2 t 2 ( 2 a ) ⋅ ⋅ ( r − − r 0 ) = ( 2 a ) ⋅ ⋅ ( v 0 t + 1 2 a t 2 ) = 2 t ( a ⋅ ⋅ v 0 ) + a 2 t 2 = v 2 − − v 0 2 ∴ ∴ v 2 = v 0 2 + 2 ( a ⋅ ⋅ ( r − − r 0 ) )