Lecture 9
Review for Exam I
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Exam 1 Review
• Chapter 1 motion diagrams, unit conversion
• Chapter 2 motion in 1-dimension, constant
velocity, constant acceleration
1. What is the difference between speed and velocity?
A.
Speed is an average quantity while velocity is not.
B.
Velocity contains information about the direction of motion while speed
does not.
C.
Speed is measured in mph, while velocity is measured in m/s.
D.
The concept of speed applies only to objects that are neither speeding
up nor slowing down, while velocity applies to every kind of motion.
E.
Speed is used to measure how fast an object is moving in a straight
line, while velocity is used for objects moving along curved paths.
Slide 1-2
Chapter 1
• Particle model of an object in motion
If Sam walks 100 m to the West, then 200 m to the South, his net displacement
vector has a magnitude of _________ and makes an angle of ________ with
respect to the x-axis
Slide 1-6
Checking Understanding
Two runners jog along a track. The positions are shown at 1 s time
intervals. Which runner is moving faster?
Slide 1-18
Speed and Velocity
Velocity is a vector !
Problem
• Alice is sliding along a smooth, icy road on
her sled when she suddenly runs headfirst
into a large, very soft snowbank that
gradually brings her to a halt. Draw a
graph of her velocity versus time and her
position versus time.
1. The slope at a point on a position-versus-time graph of an
object is
A. the object’s speed at that point.
B. the object’s average velocity at that point.
C. the object’s instantaneous velocity at that point.
D. the object’s acceleration at that point.
E. the distance traveled by the object to that point.
F. Homework Problem 2: 21
Slide 2-3
The area under a velocity-versus-time graph of an object is
A. the object’s speed at that point.
B. the object’s acceleration at that point.
C. the distance traveled by the object.
D. the displacement of the object.
E. This topic was not covered in this chapter.
F. Homework question 2.14 and 15
Slide 2-5
Acceleration
Free Fall
m
a y   g  9.80 2
s
Free Fall
a y   g  constant
v y (t )  viy  gt
1 2
y (t )  yi  viy t  gt
2
Examples
Spud Webb, height 5'7", was one of the shortest basketball
players to play in the NBA. But he had an impressive vertical leap;
he was reputedly able to jump 110 cm off the ground. To jump this
high, with what speed would he leave the ground?
A football is punted straight up into the air; it hits the ground
5.2 s later. What was the greatest height reached by the ball?
With what speed did it leave the kicker’s foot?
Passengers on The Giant Drop, a free-fall ride at Six Flags Great
America, sit in cars that are raised to the top of a tower. The cars
are then released for 2.6 s of free fall. How fast are the
passengers moving at the end of this speeding up phase of the
ride? If the cars in which they ride then come to rest in a time of
1.0 s, what is acceleration (magnitude and direction) of this
slowing down phase of the ride? Given these numbers, what is
the minimum possible height of the tower?
Slide 2-31
Additional Examples
When you stop a car on icy pavement, the acceleration of your car
is approximately –1.0 m/s². If you are driving on icy pavement at
30 m/s (about 65 mph) and hit your brakes, how much distance
will your car travel before coming to rest?
As we will see in a future chapter, the time for a car to come to
rest in a collision is always about 0.1 s. Ideally, the front of the car
will crumple as this happens, with the passenger compartment
staying intact. If a car is moving at 15 m/s and hits a fixed
obstacle, coming to rest in 0.10 s, what is the acceleration? How
much does the front of the car crumple during the collision?
Slide 2-38
Vector Components
Ax  A cos 
y
Ay  A sin 
A
Ay
θ
Ax
x
Given A and θ we found Ax and Ay
Given Ax and Ay, find A and θ
y
A  Ax 2  Ay 2
 Ay 
  tan  
 Ax 
1
Ay
θ
Ax
x
Adding vectors numerically
C  A B
Cx  Ax  Bx
C y  Ay  By
Also called algebraic addition
What would subtraction look like?
Scalar multiplication?