Lecture 4 - Linear Kinematics

Question 1

Change in location can be described with two components

Answer 1

Distance: the actual path taken (this is a scalar)

Displacement: measured in a straight line from start to finish (this is a vector)

Question 2

Speed =

Answer 2

distance traveled/change in time (scalar)

Question 3

Velocity =

Answer 3

change in position/change in time = Δ position/Δ time

Question 4

Velocity formula =

Velocity units =

Answer 4

V = displacement/change in time = d/Δt (vector)

Position2 - position1/ time2- time1

Units: m/s

Question 5

Acceleration =

Answer 5

change in velocity/time (vector)

the rate of change in linear velocity

Question 6

Acceleration formula =

Answer 6

A = V2 - V1/t

Question 7

Units for acceleration =

Answer 7

Units: m/s^2

Question 8

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

Answer 8

True

Question 9

is Acceleration always related to the direction that you’re going

Answer 9

Acceleration isn’t always related to the direction that you’re going

Question 10

Negative acceleration:

Answer 10

slowing down in a positive direction, speeding up in a negative direction

Question 11

Positive acceleration:

Answer 11

slowing down in a negative direction, speeding up in a positive direction

Question 12

what is Instantaneous velocity:

Answer 12

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.

Question 13

what are the two common approaches to determining instantaneous values:

Answer 13

graphical approximation

numerical estimation

Question 14

graphical approximation:

Answer 14

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

Question 15

Graphical Approximation;

Direction and Magnitude of Velocity

Answer 15

A downward slope indicates a negative velocity, while an upward slope indicates a positive velocity.

Question 16

Graphical Approximation;

Velocity = 0

Answer 16

Sections where the curve changes direction or is parallel to the time axis represent points where the velocity is zero.

Question 17

Graphical Approximation;

Steepness and Magnitude of Velocity

Answer 17

A steeper slope (closer to vertical) corresponds to a greater magnitude of velocity, indicating a faster rate of change.

Question 18

Graphical Approximation;

Steepest Point

Answer 18

The steepest point on the curve represents either a minimum (negative slope) or a maximum (positive slope) velocity.

Question 19

A linear change in displacement =

Answer 19

a constant velocity

Question 20

Numerical Estimation:

Answer 20

finding instantaneous slopes from sampled data

Question 21

Most kinematic data describing human motion is …

Answer 21

“sampled”; collected repetitively, at even time spacing, at fractions of a second

Question 22

Two common approaches for finding these slopes (in numerical estimation) are:

Answer 22

over 1 sample interval (simple finite difference), or over 2 sample interval (first central finite difference)

Question 23

Simple Finite Difference:

Answer 23

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

​

Question 24

First Central Finite Difference:

Answer 24

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.

Question 25

Average:

Answer 25

Value for a variable over the whole time period

Question 26

Average velocity =

Answer 26

Average velocity = final displacement/total time

Question 27

Practice question on page 28