Chapter 2 Motion in one dimension Kinematics Dynamics
Chapter 2 Motion in one dimension Kinematics Dynamics
Section2 -3 Position, velocity and acceleration vectors 1。 Position vector At any particular time t, the Z particle can be located by its X, y and z coordinates, which are the three components of the posItion vector k F=xi+y计+zk y X where i, and k are the Fig 2-11 cartesian unit vectors
At any particular time t, the particle can be located by its x, y and z coordinates, which are the three components of the position vector : where , and are the cartesian unit vectors. Section2-3 Position, velocity and acceleration vectors 1. Position vector k j i r → r = x i+ y j+ z k x y z Fig 2-11 i j k r O
2 Displacement(位移) We defined the displacement y t vector Ar as the change in position vector from t, to t2 t △F=- O x Fig 2-12 Note: 1) Displacement is not the same as the distance traveled by the particle 2)The displacement is determined only by the starting and ending points of the interval
We defined the displacement vector as the change in position vector from t1 to t2 . 2. Displacement (位移) 2 1 r r r = − r Note: 1) Displacement is not the same as the distance traveled by the particle. 2) The displacement is determined only by the starting and ending points of the interval. y z 1 r 1 t 2 t= t t= x Fig 2-12 2 r s O r
扩(=x+y1j+1k =xi+vitek Then the displacement is =(x2-x1)i+(y2-y1)j+(z2-21k Direction: from start point to end point Magnitude: A-=VAx+Ay2+A22
2 2 2 Magnitude : r = x +y +z Direction: from start point to end point if r x i y j z k 1 = 1 + 1 + 1 r x i y j z k 2 = 2 + 2 + 2 2 1 r r r = − Then the displacement is x x i y y j z z k ( ) ( ) ( ) = 2 − 1 + 2 − 1 + 2 − 1
The relationship between△fand△s In general △r≠△S △s Can △F=△s Yes. for two cases 1)1D motion without 1ox changing direction 2)When△t→>0 after take limit: dr=ds
The relationship between and : r s 1 r P1 2 r P2 r x y O z r s s In general, Can ? r = s Yes, for two cases: 1) 1D motion without changing direction 2) When after take limit: t → 0, dr = ds