苹南癢掌大 但博学求回新 South chi na Agricul tural Uni versity Summarizing Two kind of problem on kinematics of particle 1. Have known movement function, how can get velocity and acceleration? r(t) (t) a(t) By derivative 16
D e p. p h y sic s D e p. p h y sic s D e p. p h y sic s 16 Summarizing: Two kind of problem on kinematics of particle 1. Have known movement function, how can get velocity and acceleration? r(t) v(t) a(t) dt dr dt dv By derivative
③革由接掌大孝 但博学求回新 South chi na Agricul tural Uni versity 例〕平静的湖面上有一小船,一人在湖边处 有一定高度的岸上以匀速率v收绳子,使小船 向岸边靠拢,求小船的运动速度。 解:选取坐标如图,0是固定点。有: dL (这是本题的关键)v0= x=√D2-H2 dL dh L L L H 负号表示v的方向与x轴的正方向相反。 L。ax L 0 xat 2 L 2 H 2 2
D e p. p h y sic s D e p. p h y sic s D e p. p h y sic s 17 〔例〕平静的湖面上有一小船，一人在湖边处 有一定高度的岸上以匀速率v0收绳子，使小船 向岸边靠拢，求小船的运动速度。 x 0 v H L 0 解：选取坐标如图，O是固定点。有： dt dx v dt dL （这是本题的关键） v 0 2 2 x L H 0 2 2 v x L L H dt dL L dt dx v 3 2 0 2 3 2 0 2 2 0 2 0 2 0 2 0 0 x H v x L v x v x Lv v x v x dt Lv dx xdt v dL dt dv a 负号表示v的方向与x 轴的正方向相反
③举南演掌大 但博学求回新 South chi na Agricul tural Uni versity 2. Have known acceleration, how can get velocity movement function? a=→如=ad=+!adt =面→=动=+动 o By integral 18
D e p. p h y sic s D e p. p h y sic s D e p. p h y sic s 18 2. Have known acceleration, how can get velocity, movement function? t t v v dv adt 0 0 dt dv a t t v v adt 0 0 t t r r dr vdt 0 0 dt dr v t t r r vdt 0 0 By integral
③革由接掌大孝 但博学求回新 South chi na Agricul tural Uni versity 〔例〕列车沿一水平直线运动,刹车后列车的加速度a=-kv,k为一正 常数,刹车时的车速为v0,求刹车后列车最多能行进多远? 解: dv dy dx k dt dx dt dx 即 X av 积分得dx --d 0 max 19
D e p. p h y sic s D e p. p h y sic s D e p. p h y sic s 19 解： kv dx dv v dt dx dx dv dt dv a 即 dv k 1 dx 积分得 dv k 1 dx 0 v x 0 0 max k v x 0 max 〔例〕列车沿一水平直线运动，刹车后列车的加速度 a = - kv，k为一正 常数，刹车时的车速为 v0，求刹车后列车最多能行进多远？
革擦大寧 但博学一求宣倒新 South chi na Agricul tural Uni versity 4 Relative motion Based on the classical theol spatial coordinates are absolute and give identical readings for all observers @time is a universal coordinate having identical values for all observers 20
D e p. p h y sic s D e p. p h y sic s D e p. p h y sic s 20 4. Relative motion • Based on the classical theory: ①spatial coordinates are absolute and give identical readings for all observers. ②time is a universal coordinate having identical values for all observers