Chapter 2: Kinematics
Description of Motion
2.1 Distance and Speed: Scalar
Quantities
Distance is the path length traveled from one
location to another. It will vary depending on the
path.
Distance is a scalar quantity—it is described only by
a magnitude.
2.1 Distance and Speed: Scalar
Quantities
Average speed is the distance traveled divided by
the elapsed time:
2.1 Distance and Speed: Scalar
Quantities
Since distance is a scalar, speed is also a scalar
(as is time).
Instantaneous speed is the speed measured over
a very short time span. This is what a
speedometer reads.
2.1 Speed Practice
1.
You are driving to Dorney Park (25 miles away), how long will it take if
your average speed is 56 mph?
2.
If I drive to Wawa (4.8 miles away) at the speed limit (50 mph), how
long will it take? If I drove at 55 mph how much time would I save?
3.
If your friend got in their car and drove from their house to yours (6.00
miles) in 8.05 minutes, did they break the speed limit (find in MPH)?
(Assume speed limit = 45 mph)
2.2 One-Dimensional Displacement and
Velocity: Vector Quantities
A vector has both magnitude and
direction. Manipulating vectors
means defining a coordinate
system, as shown in the diagrams
to the left.
2.2 One-Dimensional Displacement
and Velocity: Vector Quantities
Displacement is a vector that points from the
initial position to the final position of an object.
2.2 One-Dimensional Displacement
and Velocity: Vector Quantities
Note that an object’s position coordinate may be
negative, while its velocity may be positive; the
two are independent.
Symbols!
2.2 One-Dimensional Displacement and
Velocity: Vector Quantities
For motion in a straight line with no reversals,
the average speed and the average velocity
are the same.
Otherwise, they are not; indeed, the average
velocity of a round trip is zero, as the total
displacement is zero!
2.2 One-Dimensional Displacement
and Velocity: Vector Quantities
Different ways of visualizing uniform velocity:
2.2 One-Dimensional Displacement
and Velocity: Vector Quantities
This object’s velocity is
not uniform. Does it
ever change direction,
or is it just slowing down
and speeding up?
2.2 Vector Practice
1.
What is the avg. velocity for Line A?
2.
Avg. velocity for Line B?
3.
Avg. velocity for Line C?
4.
You throw a ball vertically upward such that it travels 7.1 m to its
maximum height. If the ball is caught at the initial height 2.4 s after
being thrown, what is its average velocity?
5.
A boy runs 30 m east, 40 m north, and 50 m west. The magnitude of
the boy’s net displacement is:
a)
b)
c)
6.
Between 0 and 20 m
Between 20 m and 40 m
Between 40 m and 60 m
What was the above boy’s net displacement?
2.3 Acceleration
Acceleration is the rate at which velocity changes.
2.3 Acceleration
Acceleration means that the speed of an object is
changing, or its direction is, or both.
2.3 Acceleration
Acceleration may result in an
object either speeding up or
slowing down (or simply
changing its direction).
2.3 Acceleration
If the acceleration is constant, we can find the
velocity as a function of time:
Think of the vo as (Velocityoriginally)
2.3 Acceleration Practice
1.
An automobile traveling at 15.0 m/s along a straight, level road
accelerates to 25.0 m/s in 6.00s. What is the magnitude of the car’s
average acceleration in meters per second squared?
2.
A sports car can accelerate from 0.0 to 35 m/s in 3.9s. What is the
magnitude of the avg. acceleration of the car in meters per second
squared?
3.
If the car can accelerate at a rate of 7.2 m/s2, how long does it take to
accelerate from 0.0 to 25 m/s?b
2.4 Kinematic Equations
(Constant Acceleration)
From previous sections:
2.4 Kinematic Equations
(Constant Acceleration)
Substitution gives:
and:
2.4 Kinematic Equations
(Constant Acceleration)
These are all the equations we have derived for
constant acceleration. The correct equation for a
problem should be selected considering the
information given and the desired result.
2.4 Kinematic Practice
Page 61: #62-65
2.4 Kinematic Practice
62. A car accelerates from rest at a constant rate of 2.0 m/s2 for 5.0s. (a) What
is the speed of the car at the end of that time? (b) How far does the car travel in
this time?
x = xo =
v= a=
t = vo =
2.4 Kinematic Practice
63. A car travelling at 25 mi/h is to stop on a 35-m-long shoulder of the road.
(a) What is the required magnitude of the minimum acceleration? (b) How
much time will elapse during this minimum deceleration until the car stops?
x = xo =
v= a=
t = vo =
2.4 Kinematic Practice
64. A motorboat travelling on a straight course slows uniformly from 60
km/h to 40 km/h in a distance of 50 m. What is the boat’s acceleration?
x = xo =
v= a=
t = vo =
2.4 Kinematic Practice
65. The driver of a pickup truck going 100 km/h applies the brakes, giving the
truck a uniform deceleration of 6.50 m/s2 while it travels 20.0 m. (a) What is the
speed of the truck in kilometers per hour at the end of this distance? (b) How
much time has elapsed?
x = xo =
v= a=
t = vo =
2.5 Free Fall
An object in free fall has a constant
acceleration (in the absence of air
resistance) due to the Earth’s gravity.
a = -9.8 m/s2
This acceleration is directed
downward.
2.5 Free Fall
The effects of air resistance are
particularly obvious when
dropping a small, heavy object
such as a rock, as well as a larger
light one such as a feather or a
piece of paper.
However, if the same objects are
dropped in a vacuum, they fall
with the same acceleration.
2.5 Free Fall
Here are the constant-acceleration equations for
free fall:
The positive y-direction has been chosen to be
upwards. If it is chosen to be downwards, the
sign of g would need to be changed.
2.5 Free Fall Practice
Page 63: #92, 95-97
2.5 Free Fall Practice
92. A student drops a ball from the top of a tall building; the ball takes 2.8s to
reach the ground. (a) What was the ball’s speed just before hitting the ground? (b)
What is the height of the building?
y = yo =
v= g=
t = vo =
2.5 Free Fall Practice
95. (The length of a dollar is 15.7 cm, and the average human reaction time is
about 0.2 s) Is the trick a good deal for the fellow student? Justify.
y = yo =
v= g=
t = vo =
2.5 Free Fall Practice
96. A boy throws a stone straight upward with an initial velocity of 15 m/s. What
maximum height will the stone reach before falling back down?
y = yo =
v= g=
t = vo =
2.5 Free Fall Practice
97. In exercise 96, what would be the maximum height of the stone if the boy and
the stone were on the surface of the Moon, where the acceleration due to gravity
is only 1.67 m/s2?
y = yo =
v= g=
t = vo =
Summary of Chapter 2
Motion involves a change in position; it may be
expressed as the distance (scalar) or
displacement (vector).
A scalar has magnitude only; a vector has
magnitude and direction.
Average speed (scalar) is distance traveled
divided by elapsed time.
Average velocity (vector) is displacement divided
by total time.
Summary of Chapter 2
Instantaneous velocity is evaluated at a particular
instant.
Acceleration (vector) is the time rate of change of
velocity.
Kinematic equations for
constant acceleration:
Summary of Chapter 2
An object in free fall has a = –g.
Kinematic equations for an object in free fall: