Chapter 5 Flashcards
What is algebraic geometry?
Describes geometry (points, lines, shapes) using algebra
What is the equation for a rectilinear line?
Y = mx + b
The slope of a line on a graph with position on the y axis and time on the x axis denotes.. ?
Velocity
The slope of a line with velocity on the y axis and time on the x axis denotes…?
Acceleration
What is a time-series plot?
Used to graph a time-series analysis
What techniques can be used to find the instantaneous slope of a line?
Finite differences
Curve fitting (Moving arc)
Describe the finite differences technique
This method involves calculating the slope from tn-1 to tn and then from tn to tn+1 and then takes the average of the two slopes by dividing them by 2.
What is the most effective way to reduce error when using the finite differences technique?
Increase the sampling frequency.
What data is derived from the first, second and third derivatives of 5-point moving arc data?
First: position
Second: velocity
Third: acceleration
What are inverse dynamics? What are forward dynamics?
Inverse dynamics analyze motion to get the force that was applied to cause the motion.
Linear dynamics predict a motion by applying force.
(Think of cause and effect)
What is the term describing how to calculate the slope of a line using calculus?
Linear regression or derivation*
What is the term for finding the area under a curve using calculus?
Integration
What is the area under the curve of a velocity time graph?
Displacement
What is the equation to calculate the area of a trapezoid?
A = 1/2 (height 1 + height 2) * width
What rules are used to calculate the ares under a curve? Which is more accurate?
The trapezoid rule and Simpson’s rule (more accurate)
What is a practical use of forward dynamics?
To calculate vertical jump height from force platform data.
What is the definition of uniform motion.
When the velocity of an object is constant.
What determines a runners displacement during a stride?
1 - the vertical velocity at takeoff (flight time)
2 - The horizontal velocity at takeoff (horizontal displacement, dependent on flight time)
Develop an equation for uniform motion using the slope of a line.
Y = mx + b
V2 = V1 + at
Develop an equation for uniform motion using the area of a rectangle and a triangle
S = V1t + 1/2at(squared)
A ball is thrown in the air and rises 6 meters to its apex before falling back to the ground.
What was its vertical velocity at release?
10.85 m/s
A ball is thrown at an angle of 30 degrees above the horizontal with a velocity of 15m/s. How long does it take for the ball to reach its maximum heigh? What’s the balls maximum height? What is the total horizontal displacement of the ball?
0.76s, 2.87m, 19.86 m/s?
