VECTOR CALCULUS PARAMETRIC EQUATIONS 5 6 JACPLUS PARAMETRIC

VECTOR CALCULUS

PARAMETRIC EQUATIONS – 5. 6 JACPLUS

PARAMETRIC EQUATIONS

PARAMETRIC EQUATIONS BACKGROUND

WORKED EXAMPLE 19

ELIMINATING THE PARAMETER Worked Example 20 Methods to use: Direct substitution Trigonometric formulas

PARAMETRIC REPRESENTATIONS AND SKETCHING PARAMETRIC CURVES Worked Example 22 The parametric representation of a curve is not necessarily unique. To sketch parametric curves, CAS calculators can be used to draw the Cartesian equation of the path from the two parametric equations, even if the parameter cannot be eliminated.

POSITION VECTORS AS FUNCTIONS OF TIME – 13. 2 JACPLUS

WORKED EXAMPLE 1 CAMBRIDGE

WORKED EXAMPLES CAMBRIDGE Worked Example 2 Worked Example 3

CLOSEST APPROACH Worked Example 1 - Jacplus

COLLISION PROBLEMS Worked Example 2 - Jac. Plus

POSITION VECTORS AS A FUNCTION OF TIME – 12 B CAMBRIDGE

INFORMATION FROM THE VECTOR FUNCTION Worked Example 4 - Cambridge

WORKED EXAMPLES CAMBRIDGE Worked Example 5 Worked Example 6

VECTOR CALCULUS – 13. 3 AND 13. 5 JACPLUS Connections to the Study Design: AOS 4 – Vectors Vector Calculus §Differentiation and antidifferentiation of a vector function with respect to time and applying vector calculus to motion in a plan including projectile and circular motion

VECTOR CALCULUS

RULES FOR DIFFERENTIATING VECTORS Derivative of a sum or Derivative of a constant vector difference of vectors

DERIVATIVE OF A VECTOR FUNCTIONS

PROPERTIES OF THE DERIVATIVE OF A VECTOR FUNCTION

WORKED EXAMPLES CAMBRIDGE

WORKED EXAMPLE 3 JACPLUS

DERIVATIVE SUMMARY Velocity vector Speed Acceleration vector

WORKED EXAMPLE 4 JACPLUS

WORKED EXAMPLE 7 JACPLUS

ANTIDIFFERENTIATION THE CONSTANT VECTOR

INTEGRATION OF VECTOR FUNCTIONS Integrating a Velocity Vector w. r. t time gives a Position Vector Integrating an Acceleration Vector to gives a Position Vector

WORKED EXAMPLES CAMBRIDGE Example 13 Example 14

WORKED EXAMPLES JACPLUS Worked Example 10 Worked Example 11

WORKED EXAMPLES JACPLUS Worked Example 12

VELOCITY AND ACCELERATION FOR MOTION ALONG A CURVE – 12 D CAMBRIDGE

RECAP – FILL IN THE BLANKS Velocity Acceleration is _________ Therefore a(t), the acceleration _________, is given by Speed Distance between two points on the curve Speed is _________________. The ________ distance between two points on the curve is found using: At time t, the speed is denoted by _________

WORKED EXAMPLES Worked Example 15 Worked Example 16 Worked Example 18

WORKED EXAMPLE CAMBRIDGE Worked Example 17

WORKED EXAMPLES CAMBRIDGE Worked Example 19

WORKED EXAMPLES CAMBRIDGE Worked Example 20 Worked Example 21