Kinematics: The Mathematics of Motion

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Presentation transcript:

Kinematics: The Mathematics of Motion Readings: Chapter 2

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

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

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

Uniform motion: motion with constant velocity x t v t

Uniform motion: application Example: x Find and t

Position graph

realistic non-realistic

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

Finding position from velocity

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

Example: Find the net displacement C D A B area

x A C Velocity is the slope B t

Velocity is the slope Acceleration is the slope

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

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

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

Free fall motion - motion with constant acceleration

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