Formulas
How do you find dy/dx given x(t) and y(t)?
dy/dx = (dy/dt)/(dx/dt) = y'(t)/x'(t)
What is the definition of a parametric function?
A parametric function expresses the coordinates of a graph as separate functions of an independent variable
What is the definition of a vector?
Any quantity that possesses both a magnitude (size or length) and a direction.
Vector D = 3i - 4j and vector E = 4i - j. Compute the vector D + E
7i - 5j
A vector points away from the origin toward infinity. Some could say it points to "infinity and beyond". Name the character associated with this phrase.
Buzz Lightyear
What is the formula for v(t), given x(t).
x'(t)
Find dy/dx if x = t^2 + 1, y = t^3
3t/2
A particle has velocity v(t) = <0, 5>. What direction is it moving?
Upwards
For x(t) = 5x-2, y(t) = e^x, what is the equation of the tangent line at t=1?
y-e=e/5(x-3)
What is a vector in C++ computer programming?
A dynamic array that can change size
What is the formula for speed given a vector?
sqrt[(dy/dt)^2+(dx/dt)^2]
When is the tangent line of a parametric curve horizontal and vertical?
Vertical: dx/dt = 0
Horizontal: dy/dt = 0
When is a particle speeding up?
When velocity and acceleration components have the same sign
Connor’s position at time t can be modeled by the vector <3t^2+4t, 10t>. What is the equation for the normal line at t=1?
y-10=-1(x-7)
Who is the character in Despicable Me who exhibits both characteristics of direction and magnitude?
Vector
What is the formula for arc length given a vector?
∫sqrt[(dy/dt)^2+(dx/dt)^2]dt
True or false: dy/dx = 0/0 automatically indicates a horizontal or vertical tangent. Explain why.
False. 0/0 is an indeterminate form. Therefore, it simply means that the limits of the numerator and denominator are both zero, and the actual behavior of the tangent requires further evaluation.
Explain the difference between displacement and distance traveled
Displacement is net change from initial position, distance traveled is total length of the path
A particle moves according to x = t^2 - 2t, y = t^3 - 3t. At t=2, find:
1. The position; 2. The velocity vector; 3. The speed; 4. The acceleration vector
1. (0, 2)
2. <2, 9>
3. sqrt(85)
4. <2, 12>
What is a vector in epidemiology?
a living organism that carries and transmits an infectious pathogen from an infected host to an animal or human.
How do you find the second derivative of a parametric function?
[(d/dt)(dy/dx)]/(dx/dt)
What graph/equation do the parametric equations x = sin(t) and y = cos(t) resemble?
Unit circle
x^2 + y^2 = 1
True or false: On a straight line, constant speed indicates zero acceleration. Explain.
True, because the slope of velocity is zero/acceleration is zero
A particle’s motion follows the following equations: x(t) = t^2-4t+1, y(t) = 2t^3-9t^2+12t.
1. Find the velocity vector at t=2; 2. Find the speed at t=2; 3. At what time(s) the particle is moving only horizontally; 4. At what time(s) the particle is moving only vertically
1. <0, 0>
2. 0
3. t=1
4. Never
Describe the 8 Vector System in sports.
A training framework used in strength and conditioning that categorizes multidirectional athletic movement into 8 specific directional force vectors