Kinematics The Mathematics of Motion Readings Chapter 2

Kinematics: The Mathematics of Motion Readings: Chapter 2 1

Motion along a straight line 1 s 2 s 3 s Can be illustrated by positionversus-time graph: 4 s x Origin (x=0) 10 cm Continuous (smooth) curve x 20 cm 40 cm 70 cm 1 2 3 4 t(s) 2

Position graph x 1 sec 1 2 3 4 t(s) 2 sec 3 sec 4 sec Velocity is the same – zero acceleration Straight line – uniform motion – the same velocity Velocity is the slope 3

Position graph: uniform motion x Motions in opposite directions t(s) 4

Uniform motion: motion with constant velocity x t v 5 t

Uniform motion: application Example: x Find and t 6

Position graph 7

non-realistic 8

Instantaneous velocity Very small Instantaneous velocity: If dependence is given, then - derivative Instantaneous velocity - slope Example: 9

Finding position from velocity 10

v t The displacement is the area, displacement is positive v t Displacement is negative 11

Example: C D Find the net displacement A B area 12

x A C Velocity is the slope B t 13

Velocity is the slope Acceleration is the slope 14

Motion with constant acceleration Motion with constant velocity: Motion with constant acceleration: 15

Motion with constant velocity or constant acceleration Motion with constant velocity: Motion with constant acceleration: Useful relation: then 16

Motion with constant velocity or constant acceleration Motion with constant velocity: Motion with constant acceleration: 17

Free fall motion - motion with constant acceleration 18

Free fall motion - motion with constant acceleration At final point: 19