Kinematics

1
Kinematics
Physics 101 Lecture 03

• Todays lecture will cover Textbook Sections
  3.1-3.3

• HOMEWORK You can edit it up until Tues morning
  go to office hours.
• LAB preflights optional. Must do LECTURE
  preflights
• lecture and preflight will be combined in
  grade book. Free preflight 2

2
Force at Angle Example

• A person is pushing a 15 kg block across a floor
  with mk 0.4 at a constant speed. If she is
  pushing down at an angle of 25 degrees, what is
  the magnitude of her force on the block?

09
3
Homework Example

• Calculate the tension in the left string.

07
4
Overview

• Kinematics Description of Motion
• position and displacement
• velocity
• average
• instantaneous
• acceleration
• average
• instantaneous

10
5
Position vs Time Plots

• Gives location at any time.
• Displacement (Dx) is change in position.
• Slope (Dx/Dt) gives velocity.

x (m)
3
Position at t3, x(3)
Displacement between t1 and t5. Dx
t
4
-3
Average velocity between t5 and t1. v
12
6
Velocity vs Time Plots
v (m/s)

• Gives velocity at any time.
• Area gives displacement
• Slope gives acceleration.
• Speed s v

3
1.5
6
t
4
-3
18
7
Acceleration vs Time Plots

• Gives acceleration at any time.
• Area gives change in velocity

a (m/s2)
3
6
t
2
4
-3
21
8
Acceleration Preflights

• Is it possible for an object to have a positive
  velocity at the same time as it has a negative
  acceleration?
• 1 - Yes
• 2 - No

84 16
If the velocity of some object is not zero, can
its acceleration ever be zero ? 1 - Yes 2 -
No
86 14
24
9
Velocity ACT

• If the average velocity of a car during a trip
  along a straight road is positive, is it possible
  for the instantaneous velocity at some time
  during the trip to be negative?
• A - Yes
• B - No

Drive north 5 miles, put car in reverse and drive
south 2 miles. Average velocity is positive.
27
10
Dropped Ball
A ball is dropped from a height of two meters
above the ground.

• Draw vy vs t

34
11
Dropped Ball
x
A ball is dropped for a height of two meters
above the ground.
t
v

• Draw v vs t
• Draw x vs t
• Draw a vs t

t
a
t
36
12
Tossed Ball
A ball is tossed from the ground up a height of
two meters above the ground. And falls back down

• Draw v vs t

42
13
Tossed Ball
x

• A ball is tossed from the ground up a height of
  two meters above the ground. And falls back down

t
v

• Draw v vs t
• Draw x vs t
• Draw a vs t

t
a
t
45
14
ACT

• A ball is thrown straight up in the air and
  returns to its initial position. During the time
  the ball is in the air, which of the following
  statements is true?
• A - Both average acceleration and average
  velocity are zero.
• B - Average acceleration is zero but average
  velocity is not zero.
• C - Average velocity is zero but average
  acceleration is not zero.
• D - Neither average acceleration nor average
  velocity are zero.

48
15
Example
position vs. time
velocity vs. time
48
16
Summary of Concepts

• kinematics A description of motion
• position your coordinates
• displacement ?x change of position
• velocity rate of change of position
• average ?x/?t (xf xi) / (tf ti)
• instantaneous slope on x vs. t plot
• acceleration rate of change of velocity
• average ?v/?t (vf vi) / (tf ti)
• instantaneous slope of v vs. t

50
17
Acceleration (m/s2)

• The average acceleration is the change in
  velocity divided by the change in time.
• Instantaneous acceleration is limit of average
  velocity as Dt gets small. It is the slope of the
  v(t) plot

t
31
18
Velocity

• Slope of x vs t gives v vs t
• Area under v vs t gives Dx!
• Which plot best represents v(t)

x(t)
4s
Dx
Dt
t
5s
v(t)
v(t)
t
t
t