5.9 Kinematics, Rates of Change
Motion in a straight Line
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Key Ideas
Key Ideas
Mathematical modelling can provide effective solutions to real-life problems in optimization by maximizing or minimizing a quantity, such as cost or profit.
Derivatives and integrals describe real-world kinematics problems in two and three-dimensional space by examining displacement, velocity and acceleration.
I can explain the difference between the Instantaneous and average rate of change
Kinematics
Kinematics
https://www.geogebra.org/material/show/id/YcuVhFF2
Also referred to as motion in a straight line, this topic assumes some sort of particle or object to move back and forth along a straight line. The object has a velocity and a speed and it can accelerate, decelerate and change direction of travel. It's movement is described by a function, typically a polynomial.
Tip: A graph of S versus t can be converted into a motion diagram by rotating 90 degrees clockwise and squashing. Just be careful to remember the direction of travel e.g:
Important findings:
Important findings:
When acceleration and velocity have opposite signs, the object is slowing down.
When Velocity changes sign, the particle is changing direction.
Speed can not be negative. Velocity can, depending on the direction of travel.
Position, Velocity, Acceleration, Displacement
Position, Velocity, Acceleration, Displacement
Rates of change
Rates of change
About the difference between the average rate of change and the Instantaneous rate of change.
Displacement vs Total Distance
Displacement vs Total Distance
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