Kinematic and Vector AnalysisPHYSICSGRADE XI2016

Position of particle

Determine the displacement of particle

Velocity of particlea.Average

velocity

Instaneous Velocityas the gradient of component r vs t

Instaneous velocity as the differential from the function of position

Determine the position from velocity

Displacement as the area under the graph v-t

Acceleration Average acceleration

Instaneous Acceleration Instaneous acceleration define as the gradient of v(t) graph

Instaneous acceleration is the differential of the velocity function to the respect of time

Determine velocity from a-t graph

A-t graph

Homework time…1. A particle moves based on the following equation :

r(t) = 3t2 − 2t + 1, t in second and r in meter.Determine : a. Velocity at t = 2 secs b. Average velocity between t = 0 sec to 2 secs

2. A particle moves based on the following equation :

If the initial position at the center of coordinate, determine the position after 3 secs

Angular Velocity

Angular velocity is defined as the result of the angular displacement devided by time

Instaneous Angular velocity is the differential of position with respect to the time

Angular position fromangular velocity

Angular accelerationMenentukan Besar Percepatan Sudut dari Kemiringan Grafik ω-t

ß is the angle between ω-t graph vs t axis.

Determine angular velocity from acceleration

ω0 is the initial angular velocity (ω at t = 0).

CIRCULAR MOTION

Tangential Acceleration

Total acceleration

Direction

KINEMATIC CIRCULAR MOTION

Exercise Convert to radian : 900 and 2700

Convert to radian/second : 120 rpm and 60 rpm A circular motion with angular acceleration 2 rad/s2. If it starts at rest.

Determine :a) Angular acceleration after it moved 5 secondsb) Angular position after it moved 5 seconds

PROJECTILE MOTION

Position and velocity equation for projectile

At X axis

At Y axis

What about the velocity at certain time

Magnitude of Velocity

Direction of velocity

How to determine the maximum heigth and the maximum range of motion?

Coordinate for maximum

height

Time taken for maximum range (t0a)

t0H is time taken at maximum heigth

Maximum range ( R )

See the following figure about projectile motion. The initial velocity is 100 m/s and the elevation 370.

1. Initial velocity to the respect of X-axis2. Initial velocity to the respect of Y-axis3. Velocity at t = 1 second4. Direction of velocity to the respect of horizontal 5. Heigth of bullet at t = 1 second6. Horizontal range of bullet at t = 1 second7. Maximum heigth8. Maximum range9. Time taken to reach maximum heigth10.Velocity at maximum heigth11.Time taken to reach maximum range