Physics 2111
Unit 1
Outline for this unit: Displacement, Velocity, Acceleration – graphically
Displacement, velocity, acceleration - numerically
1-D Kinematics with constant acceleration
Free-fall
Mechanics Lecture 1, Slide 1
Mechanics Lecture 1, Slide 2
Think of what the position graph would look like for someone who started 10 meters from the origin and walked away at 2 meters per second.
po
siti
on
Displacement and Velocity in One Dimension
time
Mechanics Lecture 1, Slide 3
Displacement (rise)
Time taken (run)
Displacement and Velocity in One Dimension
Rise
= Slope
Run
Prelecture Example
Mechanics Lecture 1, Slide 4
Prelecture Example
Mechanics Lecture 1, Slide 5
Speed = |v(t)| when moving in one direction
The v(t) vs. t plot is just the
slope of the x(t) vs. t plot
Displacement and Velocity in One Dimension
Mechanics Lecture 1, Slide 6
Definition:
• Speed = path / time
• Average Velocity = displacement / time
Mechanics Lecture 1, Slide 7
Acceleration
Mechanics Lecture 1, Slide 8
For the Displacement and Velocity curves shown on the left, which is the correct plot of acceleration vs. time?
A
B
Checkpoint 1
Mechanics Lecture 1, Slide 9
Example Problem 1.1
The position in meters of an object moving along a straight line is given by the equation
x = 6m + 9.0m/sec2*t2 -2.0m/sec*t -6.0m/sec3*t3 .
a) What is its average velocity between 2 seconds and 4 seconds? b) What is its instantaneous velocity at t=3sec?
Mechanics Lecture 1, Slide 10
Constant Acceleration
constant
a(t) = a
Mechanics Lecture 1, Slide 11
Example Problem 1.2
You are cruising along at 15m/sec, when you pass a police car stopped along the side of the road. 10 meters after you pass the car, you begin to accelerate at 2.0m/sec2. How far are you from the police car 5 seconds after you begin to accelerate?
1) Draw a sketch 2) Draw a coordinate
system 3) What are you looking
for?
Mechanics Lecture 1, Slide 12
At t = 0 a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves 1 foot between t = 0 sec and t = 1 sec.
How far does it move between t = 1 sec and t = 2 sec?
A) 1 foot B) 2 feet C) 3 feet D) 4 feet E) 6 feet
Checkpoint 2
Mechanics Lecture 1, Slide 13
At t = 0 a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves 1 foot between t = 0 sec and t = 1 sec.
How far does it move between t = 3 sec and t = 4 sec?
A) 3 feet B) 4 feet C) 7 feet D) 9 feet E) 16 feet
Follow up
Free fall
Straight forward example of constant
acceleration is “free fall”
If air resistance is negligible, all
objects fall with the same rate of
acceleration
g = 9.81m/sec2
Mechanics Lecture 1, Slide 14
Example Problem 1.4
You drop a small rock from the top of
a 300meter tall building.
What is its velocity after 5
seconds?
What is its position after 5
seconds?
Mechanics Lecture 1, Slide 15
(Note: This is a pretty tall building. The Sears Tower is 527 meters tall.)
Example Problem 1.5
You drop a small rock from the top of
a 300meter tall building.
How long does it take to
hit the ground?
What is its velocity just
before it hits?
Mechanics Lecture 1, Slide 16
Example Problem 1.6
You throw a small rock downwards
with a velocity of 20m/sec from the
top of a 300meter tall building.
How long does it take to
hit the ground?
What is its velocity just
before it hits?
Mechanics Lecture 1, Slide 17
Question
You throw a small rock upwards with a velocity of
20m/sec from the top of a 300meter tall building.
What is its velocity just before it hits?
Mechanics Lecture 1, Slide 18
We previously calculated the final velocity
of the rock when we threw is downwards at
20m/sec as 79m/sec. How will that
compare to our final velocity now that we’re
throwing it upward?
a) vf > 79m/sec
b) vf = 79m/sec
c) vf < 79m/sec
Example Problem 1.7
You throw a small rock upwards with
a velocity of 20m/sec from the top of
a 300meter tall building.
What is its velocity just before it hits?
Mechanics Lecture 1, Slide 19
How long does it take to hit the
ground?
Example Problem 1.8 (Ball Toss)
Mechanics Lecture 1, Slide 20
A person throws a ball vertically upward into the air with an initial velocity of 15.0 m/s.
How high does the ball go?
How long is the ball in the air before it comes back to the persons hand?
Example 1.9 (Non-constant acceleration)
Can use kinematic concepts with non-
constant acceleration.
Mechanics Lecture 1, Slide 21
Example:
a(t) = 8.0m/sec2 – 0.4m/sec3*t
At t = 0sec, x=0m, v=20m/sec.
What is xf at t=5sec?
Example 1.10 (When does clock start?)
Objects don’t always start to move at
t = 0.
Mechanics Lecture 1, Slide 22
Example:
3 sec after t=0, a cart initially at
rest begins to accelerate at
a=2m/sec2.
What is its position at t=6sec?
Example 1.11 (2 Carts, 2 Times)
Mechanics Lecture 1, Slide 23
At t=0, blue toy cart starts with a velocity of
10m/sec and an acceleration of -2m/sec2.
4 sec later, a red toy cart starts from the
same position and moves with a constant
velocity of 6m/sec in the same direction.
How long before the blue cart briefly
comes to rest?
How long before the carts collide?
Motion Diagrams
Mechanics Lecture 1, Slide 24
Imagine you took multiple exposures
every second of an object as it moved.
You are driving your fire-engine red Toyota Echo (with the great CD player) along at 50km/hr (14m/s) when a dog runs out into the road in front of you. It takes you 0.5 second to react and slam on the brakes. The plot to the right shows your velocity as function of time. How far will you travel before coming to a stop?
Example 1.12 (Position from velocity)
Mechanics Lecture 1, Slide 25
Method I: Algebraically
Breaking Distance of a Car
Mechanics Lecture 1, Slide 26
A B
Method II: Graphically
Breaking Distance of a Car
Mechanics Lecture 1, Slide 27
Find the area under
the velocity vs time
curve
Integrate!
