Linear Kinematics

1
Linear Kinematics

• Chapter 2 in the text

2
KINEMATICS
Next Class
3
Scalars

• A measure that only considers magnitude
• Does not consider direction
• E.g., a distance of 15 meters is a scalar measure

• The line is 15 meters but has no direction

4
Vectors

• Describes both a magnitude and direction
• E.g., a displacement of 15 meters in the positive
  direction is a vector.
• Represented by arrows, in which the length
  represents magnitude and orientation represents
  direction.

• The arrow is 15 meters in the positive direction

5
Distance

• A measure of the length of the path followed by
  an object from its initial to final position.
• A scalar quantity (no direction)

6
Speed

• The rate of motion of an object
• The rate at which an objects position is
  changing.
• A scalar quantity (no direction)

7
Displacement

• The straight-line distance in a specific
  direction from the starting position to the
  ending position.
• A vector quantity (must have direction)
• As the crow flies

8
Velocity

• The rate of motion in a specific direction
• Same as speed but with a direction
• A vector quantity

9
Distance vs. Displacement
Distance
Displacement
10
Speed vs. Velocity
It took Billy 3.5 hours in total to walk 5 km
North and 10 km East. What was Billys average
speed and average velocity?
Speed
Velocity
11
Acceleration

• The rate at which an objects speed or velocity
  changes.
• When an object speeds up, slows down, starts,
  stops, or changes direction, it is accelerating.
• Always a vector quantity (has direction)

12
Acceleration

• The direction of motion does not indicate the
  direction of acceleration.
• An object can be accelerating even if its speed
  remains unchanged. The acceleration could be due
  to a change in direction not magnitude.

13
Midterm Example
Bolt runs 200 m in 19.19 seconds. Assume he ran
on the inside line of lane 1, which makes a
semicircle (r 36.5 m) for the first part of the
race. He runs the curve in 11 s.
Circle Circumference 2?r Circle Diameter
2r r is radius

1. What distance was run on the curve?
2. What was his displacement after the curve?
3. Total distance?
4. Total displacement?
5. Average velocity on the curve?
6. Average speed on the curve?
7. Average velocity for the race?
8. Average speed for the race?

Start
36.5 m
Finish
14
Midterm Example
Bolt runs 200 m in 19.19 seconds. Assume he ran
on the inside line of lane 1, which makes a
semicircle (r 36.5 m) for the first part of the
race. He runs the curve in 11 s.
Circle Circumference 2?r Circle Diameter
2r r is radius

1. What distance was run on the curve?
2. What was his displacement after the curve?
3. Total distance?
4. Total displacement?
5. Average velocity on the curve?
6. Average speed on the curve?
7. Average velocity for the race?
8. Average speed for the race?

Start
36.5 m
Finish
15
Instantaneous Velocity

• The average velocity over an infinitely small
  time period.
• Determined using Calculus
• The derivative of displacement
• The slope of the displacement curve

16
Instantaneous Acceleration

• The average acceleration over an infinitely small
  time period.
• Determined using Calculus
• The derivative of velocity
• The slope of the velocity curve

17
Slope
Y
(4,8)
8
(0,0)
X
4
Slope rise ?Y Y2 Y1 8 0 8
2 run ?X X2 X1 4 0
4
18
Velocity is the slope of Displacement
Y
(4,8)
8
Displacement (m)
(0,0)
X
4
Time (s)
Average Velocity rise ?D D2 D1 8
0 8 m 2 m/s run ?t
t2 t1 4 0 4 s
19

1. The displacement graph on the previous slide was
   a straight line, therefore its slope was 2 at
   every instant.

1. Which means the velocity at any instant is equal
   to the average velocity.

1. However if the graph was not straight the
   instantaneous velocity could not be determined
   from the average velocity.

20
Average vs. Instantaneous
Average Velocity rise ?D D2 D1 8
0 8 m 2 m/s run ?t
t2 t1 4 0 4 s

• Read Ch. 6 pages 147-158 for next class