1. Learning Intention: To understand Rates of Change and how calculus is used to study the motion of objects (kinematics).
Success Criteria:
Solve problems which involve distance, speed and acceleration using differentiation and integration

2. dy/dx is the rate of change of y with respect to x.
Gradient of a line is the measure of how quickly y is changing in relation to x.
dy/dx is the rate of change of y with respect to x.
Use this concept for other variables.
The area covered by a chemical spillage at a given time of t in seconds is given by
A = t(t2 - 2) m2, t>2.
The rate of change of the area covered, A, with respect to the time, t, is dA/dt.
If A = t(t2 - 2) = t3 – 2t
Then dA/dt = 3t2 – 2
E.g. the rate at which the area covered by the chemical spill is changing after 12 seconds is
dA/dt = 3× 122 – 2 = 430m2/s dx

3. Kinematics – study of motion
Velocity(speed) is the rate of change of distance with respect to time
Distance is termed, s.Units for distance (s) is ____
Velocity, v = ds/dt units _____
Acceleration is the rate of change of ______ with respect to time.
a = dv/dt units ______
In a practical context, where does motion normally start from?
Origin
Usually Horizontal motion
If motion is vertical, origin is ground level
‘Initially’ means at time t=0, ie, when motion usually starts. Positive motion means above or to the right of the origin
Negative motion – below or to the left of the origin
When s = 0, the object is at the origin.
Velocity
Positive velocity – right or up
Negative velocity – left or down
If the velocity is zero, ie, v=0 then the object is stationary, or ‘at rest’.
Acceleration
Positive – speeding up
Negative – slowing down
If a = 0, the object is travelling at a constant speed.
e.g A on board

4. Objects hit or thrown through the air have vertical and horizontal velocity components (physics-kinematics).
Use this info the calculate times to targets and distances vy vx
260m
Vy is affected by gravity, which is the acceleration due to gravity. Vx is not affected by acceleration due to gravity.
a = -10m/s2
Remember you can use v = s t