Two-and Three-Dimentional Motion (Kinematic)

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1 Two-and Three-Dimentional Motion (Kinematic)

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3 Position Vector y C The location of a particle relative to the origin of a coordinate system is given by a position vector r , which in unit – vector notation is A B x D Student Activity : State position points A, B, C, D using unit-vector notation.

4 Position as a function of time Example :
Student Activity : Determine position of a particle that has function of time as stete above at : a. Initially b. t = 2 second c. t = 4 second

5 Displacement If a particle moves so that its position vector changes from to , the particle’s displacement is The displacement can also be written as :

6 Student Activity : Determine the displacement vector :
From point A to point C b. From point A to point B The magnitude of displacement : y C A The direction of displacement is tate in angle : B x D

7 Student Activity Suppose the position vector of a particle is given by : t is in second and r in meter. Determine the magnitude and direction of particle displacement from t1 = 1 s to t2 = 2 s

8 Average Velocity If a particle undergoes a displacement in time interval , its average velocity for that time interval is : The magnitude of average velocity is : Direction of average velocity is :

9 Student Activity A particle is moving on an x-y coordinat plane. The change of particle position follows the equation : Where t is in second and r is in meter. Determine : Vector of average velocity if particle moves from t = 0 to t = 2 s Magnitude of average velocity from t = 0 to t = 2 s c. Direction of average velocity

10 C C B B A A CONSTANT VELOCITY CONSTANT ACCELERATION Instantenous velocity = average velocity Instantenous velocity = average velocity

11 Instantaneous Velocity
When Dt is shrunk to 0, reaches a limit called either the velocity or the instantaneous velocity Dr Dt

12 How to Calculate Instantaneous Velocity
r C B2 rB1 : position when t = t rB2 : position when t = t + Dt B Dr A Or can be determine by “Deferential” function B1 Dt t Student Activity

13 Student Activity A particle is moving on an x-y coordinate plane. The change of particle position follows the equation Where t is in second and is in meter Determine : The vector instantaneous velocity at t = 2 s b. The magnitude and direction of instantaneous velocity at = 2 s

14 Kerjakan soal berikut :
Vektor posisi sebuah partikel yang bergerak dinyatakan oleh : r = 40ti + (30t-5t2)j a. Tentukan kecepatan dua detik pertama b. Tentukan kecepatan mula-mula c. Tentukan kecepatan saat t = 2 s

15 Acceleration Average acceleration
If a velocity of a particle change in time interval , its average acceleration for that time interval is : The magnitude of average acceleration is : Direction of average acceleration is : Or can be determine by “Deferential” function

16 Student Activity The velocity equation of a moving particle is stated by : v = 4ti + ( t2)j Determine the average acceleration from t = 0 to t = 2s

17 Acceleration Instantenous Acceleration v1 : velocity when t = t
v2 : velocity when t = t + Dt Or can be determine by “Deferential” function

18 Student Activity A bird flying on the XY plane with velocity that is stated by : v = (2.1 – 3.6t2)i + 5.0tj. Initially the bird is on the (0;0) Determine the vector of acceleration as time function Determine the bird acceleration at t = 2s Determine the average acceleration in interval of time from t = 0 to t = 2 s

19 Determination velocity from acceleration equation
To determine velocity from acceleration equation, we use integral function to change acceleration equation become velocity equation Integral Function to use Integral function in a simple way :

20 Student Activity A particle moves on the y axis with acceleration of a = 2t , if initially its velocity is 3 m/s, determine the velocity at t = 2 s t = 4 s

21 Determination position from velocity equation
To determine position from velocity equation, we use integral function to change velocity equation become position equation Integral Function to use Integral function in a simple way :

22 Percepatan gerak partikel dinyatakan dengan persamaan a = 2ti + 4j, a dlm m/s2. jika mula-mula partikel beada di posisi 2i + j, dalam keadaan diam, tentukan kecepatan dan posisinya saat t = 4s.

23 Sebuah partikel P bergerak dengan percepatan a
Sebuah partikel P bergerak dengan percepatan a. Tentukan vektor kecepatan dan vektor posisi P pada saat t. jika diketahui a = 15t2i + 8tj. Mula-mula partikel di titik asal dan sedang bergerak dengan kecepatan i + 2j

24 Kecepatan gerak partikel dinyatakan dalam persamaan : v = 3t2i + 4tj, mula-mula partikel berada di posisi 3j. Tentukan a. posisi partikel saat t = 3s b. percepatan partikel saat t = 2s

25 Selesai