Lecture 4 - Linear Kinematics Flashcards
Change in location can be described with two components
Distance: the actual path taken (this is a scalar)
Displacement: measured in a straight line from start to finish (this is a vector)
Speed =
distance traveled/change in time (scalar)
Velocity =
change in position/change in time = Δ position/Δ time
Velocity formula =
Velocity units =
V = displacement/change in time = d/Δt (vector)
Position2 - position1/ time2- time1
Units: m/s
Acceleration =
change in velocity/time (vector)
the rate of change in linear velocity
Acceleration formula =
A = V2 - V1/t
Units for acceleration =
Units: m/s^2
True or False: Acceleration may be positive, negative, or equal to zero, based on the direction of
motion and the direction of the change in velocity
True
is Acceleration always related to the direction that you’re going
Acceleration isn’t always related to the direction that you’re going
Negative acceleration:
slowing down in a positive direction, speeding up in a negative direction
Positive acceleration:
slowing down in a negative direction, speeding up in a positive direction
what is Instantaneous velocity:
Value for a variable at a specific instant in time
This can be determined by examining the slope of the displacement vs. time curve at that specific time.
what are the two common approaches to determining instantaneous values:
graphical approximation
numerical estimation
graphical approximation:
This method involves looking at a graph or a curve representing the variable over time
The instantaneous value can be estimated by examining the slope of the curve at a specific point
Graphical Approximation;
Direction and Magnitude of Velocity
A downward slope indicates a negative velocity, while an upward slope indicates a positive velocity.
Graphical Approximation;
Velocity = 0
Sections where the curve changes direction or is parallel to the time axis represent points where the velocity is zero.
Graphical Approximation;
Steepness and Magnitude of Velocity
A steeper slope (closer to vertical) corresponds to a greater magnitude of velocity, indicating a faster rate of change.
Graphical Approximation;
Steepest Point
The steepest point on the curve represents either a minimum (negative slope) or a maximum (positive slope) velocity.
A linear change in displacement =
a constant velocity
Numerical Estimation:
finding instantaneous slopes from sampled data
Most kinematic data describing human motion is …
“sampled”; collected repetitively, at even time spacing, at fractions of a second
Two common approaches for finding these slopes (in numerical estimation) are:
over 1 sample interval (simple finite difference), or over 2 sample interval (first central finite difference)
Simple Finite Difference:
In this method, the instantaneous slope is estimated over a single sample interval
The simple finite difference involves calculating the change in the dependent variable (e.g., displacement) divided by the change in the independent variable (e.g., time) over one sample interval.
Mathematically, it can be expressed as follows:
Instantaneous Slope= Δd/ Δt
First Central Finite Difference:
In this method, the instantaneous slope is estimated over two sample intervals, providing a more accurate approximation.
The first central finite difference involves calculating the change in the dependent variable between two adjacent points divided by the average change in the independent variable over those two points.
Mathematically, it can be expressed as follows:
Instantaneous Slope=
di+1 − di−1 / ti+1 − ti−1
where “di and ti” represent the values of the dependent and independent variables at the i-th time point, and “i” is the index corresponding to a specific time point.
Average:
Value for a variable over the whole time period
Average velocity =
Average velocity = final displacement/total time
Practice question on page 28
