The difference between|△;and△r(△E (A≡△元) △: magnitude of△F Ar: the change of length B/△ of position vectors △ x2+y2+ Note △F≠△r
The difference between and ( ): r r r r 1 r P1 2 r r P2 x y O r z 2 1 2 1 2 1 − x + y + z 2 2 2 2 2 2 r = x + y +z Note r : magnitude of r : the change of length of position vectors r ( r r ) r
When At->0. after take limit △F→)cF △产|GF △s→>C=F ∧y→d △→>=h≠l
When after take limit: t → 0, dr dr r dr → | r | | dr | → s →ds r →dr r d r → | dr | =
3. velocity and speed a. The average velocity in any interval is defined to be displacement divided by the time interval △F △t (27) when we use the term velocity we mean the instantaneous velocity b. To find the instantaneous velocity, we reduce the size of the time interval At that is M→>0 and then△r→>0. v(O)=1inF(t+△)-F() lim t→)0 △t->0 △tdt 2-9)
3.velocity and speed a.The average velocity in any interval is defined to be displacement divided by the time interval, (2-7) when we use the term velocity, we mean the instantaneous velocity. b. To find the instantaneous velocity, we reduce the size of the time interval , that is t → 0 and then . → 0 → r dt dr t r t r t t r t v t t t = = + − = → → lim lim 0 0 ( ) ( ) ( ) t r va v = t (2-9)
In cartesian coordinates dr= dx i+dy j+ dzk dr dx dv dz +=j+,k dtdt dt The vector v can also be written in terms of its components as: v=vi+vi+vk dy Vx dt vy dt v: dt (2-12)
= = + + k dt dz j dt dy i dt dx dt dr v The vector can also be written in terms of its components as: (2-11) v v v i v j v k x y z = + + dt dx vx = dt dy vy = dt dz vz = (2-12) dr = dx i+ dy j+ dz k In cartesian coordinates: