1. By Jordyn Kohl, Soumya Kamath, and Peter Ballentine
Parametric and Vector
By Jordyn Kohl, Soumya Kamath, and Peter Ballentine

2. Part 1: Parametric

3. Parametric Functions
defined: a group of quantities as functions of one or more independent variables called parameters
x = f(t)
y = g(t)
input: t
x = sin(3πt)
y = cos(5πt) -1 .5 1
1.5

4. Derivative of Parametric Equationdy dt
1st derivative: = dy dx dx dt
2nd derivative: ( ) d dt dy dx dx dt

5. √(f’(t))2 +(g’(t))2)dx Additional Terms B A
Parametric Arc Length Equation: B
√(f’(t))2 +(g’(t))2)dx A

6. Part Two: Vectors

7. Key Definitions
Vector- directed line segment with a initial and terminal point.
Component form: < x(t), y(t) >
Magnitude: Length of the vector. = x2+y2
Speed: l v l (absolute value of the velocity vector)
Average Speed: Distance divided by time elapsed.
Total distance traveled: Integrate velocity function using the bounds given and take the absolute value of the value.

8. Motion with vectors Position: s(t)= <x(t), y(t)>
Velocity: v(t)= <x’(t), y’(t)>
Acceleration: a(t)= <x’’(t), y’’(t)>
Derivative
Integration
Moving left: x’(t) is negative
Moving right: x’(t) is positive.
Moving down: y’(t) is negative
Moving up: y’(t) is positive.
At rest when x’(t)=0 and y’(t)=0