CH5: Displacement, Velocity, Acceleration Flashcards
What is Algebra?
Branch of mathematics using letters and symbols to represent numerical parameters in equations
What is Geometry?
Branch of mathematics describing points, lines, and shapes
What is Algebraic Geometry?
Describing points, lines, and shapes using algebraic equations
What does rectilinear mean?
Straight line
What does curvilinear mean?
Curved line
What is the equation for a rectilinear line?
Y = mX + b
m: slope of the line (rise/run, ∆y / ∆x)
b: constant
What is the slope of a line and velocity?
s = vt + c
s = position
t = time
v = velocity (rise/run, ∆s / ∆t)
- ∆s = displacement [change in position]
c = constant
What is the slope of a line and acceleration?
v = at + c
v = velocity
t = time
a = acceleration (rise/run, ∆v / ∆t)
c = constant
What is the slope of a position-time graph?
Slope of line is velocity
What is the slope of a velocity-time graph?
Slope of line is acceleration
Instantaneous VS average velocity
Instantaneous velocity is the velocity of an object in motion at a specific point in time, while the average velocity is a vector quantity calculated by dividing the displacement by the total time taken.
What are the two ways to calculate instantaneous slope?
- Finite Differences Technique
a. Least accurate
b. Requires very high sampling frequencies (small time intervals) to reduce error - Curve Fitting (moving arc, spline, regression)
a. Curve with known equation is fit to a series of data points
b. Derivative of equation gives instantaneous slope
What is inverse dynamics?
If we know the mass of the object, we can calculate the force applied to the object. We are working backwards (or inverse) by measuring motion and using it
to calculate force. f = ma
What is the area of a rectangle (formula)?
A = h * w
What is the area of a triangle (formula)?
A = (1/2)h * w
What does the area under the velocity-time graph represent
Displacement (Process of Integration)
What does the area under the acceleration-time graph represent
Velocity
What is the area of a trapezoid (formula)?
A = (1/2)(h1 + h2) * w
What is Simpson’s rule?
- Similar principle to finite differences technique and moving arc
– Data integrated between multiple time points before and after time point of interest - Velocity = Acceleration * Time Interval
- Displacement = Velocity * Time Interval
What is Forward Dynamics?
If we can measure force, than we can calculate or predict, using forward dynamics, the subsequent kinematics.
- Also be described by the Impulse-Momentum relation (which is part of Newton’s Second Law)
- It specifically describes a cause and effect relation – the cause is impulse, the effect is change in momentum. As momentum is mass times velocity, impulse is applied to cause a change in velocity (and subsequently displacement).
What is uniform motion?
acceleration = constant
When acceleration is constant, regardless of its value. Uniform velocity is a special case of uniform acceleration.
What is uniform velocity?
∆velocity = 0; acceleration = 0
When acceleration is zero, therefore change in velocity must be zero as well.
When does uniform motion occur?
Projectile motion = constant acceleration
- Vertical force: gravity
- Horizontal force: none (Ignore wind resistance)
Characteristics of projectile motion (on Earth)
- Vertical: a = -9.81m/s^2 (Uniform acceleration)
- Horizontal: a = 0m/s^2 (Uniform velocity)
What can be considered a projectile?
Implement, Ball, Javelin, Discus, frisbee, Human body, Vertical/horizontal jump, Running
How do you determine running speed?
Running speed = stride length * stride frequency
– Stride length – horizontal displacement between left & right feet on two successive ground contacts
What is the flight phase of running?
Time both lower limbs are off the ground
