CH5: Displacement, Velocity, Acceleration

Question 1

What is Algebra?

Answer 1

Branch of mathematics using letters and symbols to represent numerical parameters in equations

Question 2

What is Geometry?

Answer 2

Branch of mathematics describing points, lines, and shapes

Question 3

What is Algebraic Geometry?

Answer 3

Describing points, lines, and shapes using algebraic equations

Question 4

What does rectilinear mean?

Answer 4

Straight line

Question 5

What does curvilinear mean?

Answer 5

Curved line

Question 6

What is the equation for a rectilinear line?

Answer 6

Y = mX + b
m: slope of the line (rise/run, ∆y / ∆x)
b: constant

Question 7

What is the slope of a line and velocity?

Answer 7

s = vt + c
s = position
t = time
v = velocity (rise/run, ∆s / ∆t)
- ∆s = displacement [change in position]
c = constant

Question 8

What is the slope of a line and acceleration?

Answer 8

v = at + c
v = velocity
t = time
a = acceleration (rise/run, ∆v / ∆t)
c = constant

Question 9

What is the slope of a position-time graph?

Answer 9

Slope of line is velocity

Question 10

What is the slope of a velocity-time graph?

Answer 10

Slope of line is acceleration

Question 11

Instantaneous VS average velocity

Answer 11

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.

Question 12

What are the two ways to calculate instantaneous slope?

Answer 12

1. Finite Differences Technique
   a. Least accurate
   b. Requires very high sampling frequencies (small time intervals) to reduce error
2. 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

Question 13

What is inverse dynamics?

Answer 13

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

Question 14

What is the area of a rectangle (formula)?

Answer 14

A = h * w

Question 15

What is the area of a triangle (formula)?

Answer 15

A = (1/2)h * w

Question 16

What does the area under the velocity-time graph represent

Answer 16

Displacement (Process of Integration)

Question 17

What does the area under the acceleration-time graph represent

Answer 17

Velocity

Question 18

What is the area of a trapezoid (formula)?

Answer 18

A = (1/2)(h1 + h2) * w

Question 19

What is Simpson’s rule?

Answer 19

• 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

Question 20

What is Forward Dynamics?

Answer 20

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).

Question 21

What is uniform motion?

Answer 21

acceleration = constant
When acceleration is constant, regardless of its value. Uniform velocity is a special case of uniform acceleration.

Question 22

What is uniform velocity?

Answer 22

∆velocity = 0; acceleration = 0
When acceleration is zero, therefore change in velocity must be zero as well.

Question 23

When does uniform motion occur?

Answer 23

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)

Question 24

What can be considered a projectile?

Answer 24

Implement, Ball, Javelin, Discus, frisbee, Human body, Vertical/horizontal jump, Running

Question 25

How do you determine running speed?

Answer 25

Running speed = stride length * stride frequency
– Stride length – horizontal displacement between left & right feet on two successive ground contacts

Question 26

What is the flight phase of running?

Answer 26

Time both lower limbs are off the ground