Course II. Lesson 7 Applications to Physics. 7A Velocity and Acceleration of a Particle

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Cornelius Owen
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1 Course II Lesson 7 Applicaions o Physics 7A Velociy and Acceleraion of a Paricle

2 Moion in a Sraigh Line : Velociy O Aerage elociy Moion in he -ais + Δ + Δ 0 0 Δ Δ Insananeous elociy d d Δ Δ Δ 0 lim [ m/s ] [ m/s ]

3 Moion in a Sraigh Line : Acceleraion Aerage acceleraion a Δ Δ Insananeous elociy a lim Δ 0 [ m/s ] Δ Δ [ m/s ] d d Posiion Velociy Acceleraion () () o o a o d d d a d 3

Vecor and Scalar Velociy and Speed Vecor --- A quaniy ha is described by boh a magniude and a direcion. Scalar --- A quaniy ha is described by a magniude alone.

4 Vecor and Scalar Velociy and Speed Vecor --- A quaniy ha is described by boh a magniude and a direcion. Scalar --- A quaniy ha is described by a magniude alone. N Velociy and Speed Velociy --- A ecor quaniy ha refer o how fas and in wha direcion an objec is moing. Speed --- A scalar quaniy ha refers o how fas an objec is moing Velociy is speed wih a direcion. W 60 km/h A S B 60 km/h 4 E Car A and car B hae same speed bu differen elociy I go i!

5 Planner Moion Velociy and Speed Velociy of poin Q :, Velociy of poin R : Velociy of poin P: Speed of poin P: d d dy d! d, d Acceleraion Acceleraion of poin P: a! Magniude of acceleraion d d a dy d + dy d d d y, d d d d d y + d Is acceleraion a ecor? 5

6 Eample : Case of Consan Acceleraion [Eamples 7-] A ball is ossed sraigh up wih an iniial speed of 5m/s. Take he y-ais upward wih he origin a he ball s release poin. If he ime is couned from he insan when he ball is released, he posiion of he ball is gien by y( ) y0 + 0 g where y m, m/s and m/s g Deermine he ime when he ball reaches is highes posiion and wha is is heigh? The elociy A he op, we hae dy 0 d g 0 g 0 y 3 0 5m/s.6s g 9.8m/s y( ) m o.6 6

7 Eercises [ E.7- ] The posiion of a paricle moing in he -ais is gien by 3 ( ) () Find he elociy and he acceleraion a. () Inesigae he moion during 0 4. Pause he ideo and sole he problem by yourself. 7

8 Answer o he Eercises [ E.7- ] The posiion of a paricle moing in he -ais is gien by 3 ( ) () Find he elociy and he acceleraion a. () Inesigae he moion during 0 4. () d () ( ) ( )( 3) d d ( ) 6 ( ) 3 a( ) 0 d a Therefore,,

9 Course II Lesson 7 Applicaions o Physics 7B Relaed Raes 9

Eample [Eample 7-] A man is pulling a boa from he op of quay using a rope. The heigh of a man is 9 m from he waer surface and he rae of change of he rope lengh is m/s.

10 Eample [Eample 7-] A man is pulling a boa from he op of quay using a rope. The heigh of a man is 9 m from he waer surface and he rae of change of he rope lengh is m/s. Wha is he speed of he boa when he rope lengh is 5m. y Rope lengh l [m] Disance beween he quay and he boa u [m] u + 9 l Differeniae by du dl u l d d Condiions dl m/s, l 5 m, u d 5 9 Then du du 5 ( ).5 d d m/s 9m 5m??? 0

11 Eample [ Eample 7-3 ] Waer is poured ino an inered circular cone of base radius 8 cm and heigh 6 cm a he rae 3 cm 3. Wha is he rae of increase of he heigh of he waer leel when he deph is 6cm? Volume of he waer V π r h 3 Raio 8 : r 6 : h, Therefore r h V π h 3 Differeniaion by : dv dh π h d 4 d dv Condiion : 3 cm 3 /s, h 6 cm d Subsiuion dh dh 3 π 6, cm/s 4 d d 3π

12 Eercises [ E.7- ] A recangular waer ank is being filled a he consan rae of 0 liers/s. The dimensions of he ank are w m and l m. Wha is he rae of change of he heigh of waer in he ank? Pause he ideo and sole he problem by yourself.

13 Answer o he Eercises [ E.7- ] A recsngulsr waer ank is being filled a he consan rae of 0 liers/s. The dimensions of he ank are w m and and l m. Wha is he rae of change of he heigh of waer in he ank? w l dv V ( ) wl( ) wl d Differeniaion by : dv d wl d d dv Condiion : 0 lier/s 0000 cm 3 /s d By subsiuion, we hae d d wl dv d d d wl dv d cm/s 3

2.1: What is physics? Ch02: Motion along a straight line. 2.2: Motion. 2.3: Position, Displacement, Distance

2.1: What is physics? Ch02: Motion along a straight line. 2.2: Motion. 2.3: Position, Displacement, Distance Ch: Moion along a sraigh line Moion Posiion and Displacemen Average Velociy and Average Speed Insananeous Velociy and Speed Acceleraion Consan Acceleraion: A Special Case Anoher Look a Consan Acceleraion