# Describing Motion: Kinematics in one dimension - Temple

http://astro.temple.edu/~elenab/

Describing Motion:

Kinematics in one dimension

Kinematics

is a part of mechanics, which is the
description of how objects move.

Translational

motion

Reference Frame

Speed

Speed is a measure of how fast object moves,
measured by a unit of distance divided by a unit
of time.

Instantaneous Speed

Average speed doesn’t indicate the different
speeds that may have taken place during
shorter time intervals.

Average Speed

average speed

= total distance traveled/ time elapsed

Total distance traveled
= average speed X time

1.
What is the average speed of a cheetah that sprints 100 m in 4 s?
How about if it sprints 50 m in 2 s?

2.
If a car moves with an average speed of 60 km/h for an hour, it
will travel a distance of 60 km.

(a) how far would it travel if it moved at this rate for 4 h?

(b) for 10 h?

3. In addition to speedometer on the dashboard of every car is an
odometer, which records the distance traveled. If the initial
reading is set at zero at the beginning of a trip and the reading is
40 km one half hour later, what has been your average speed?

4. Would it be possible to attain the average speed in previous
example and never go faster than 80 km/h?

Velocity

When we describe speed and the
direction

of
motion, we are specifying
velocity

Instantaneous Velocity

1.
With what two physical values is the race
-
car driver
concerned? Speed or velocity?

2.
The speedometer of a car moving to the east reads 100
km/h. It passes another car that moves to the west at 100
km/h. Do both cars have the same speed? Do they have the
same velocity?

3.
During certain period of time, the speedometer of a car
reads a constant 60 km/h. Does this indicate a constant
speed or a constant velocity?

1.
How might you estimate your speed if the speedometer in
your car is broken?

2. Which of the following can be used to measure an average
speed: stopwatch, odometer, or speedometer? An
instantaneous speed?

Acceleration

We can change the velocity of something
by changing its speed; by changing its
direction or by changing its speed and its
direction.

Acceleration

average acceleration = change of velocity/time elapsed

Acceleration tells us how fast the
velocity

changes,
whereas velocity tells us how fast the
position

changes.

Motion at Constant Acceleration

Acceleration
is a rate of
change , or change per
second of velocity.

v= at

1.
Which has the greater acceleration, an airplane that goes
from 1000 km/h to 1005 km/h in 10 s, or a skateboard that
goes from 0 to 5 km/h in 1 sec?

2.
What is the acceleration of a race car that whizzes past you at
a constant velocity 400 km/h?

Falling Objects

Acceleration on Galileo Inclined Planes

Galileo found greater accelerations for
steeper inclines. The ball attains max
acceleration when the incline is tipped
vertically.

-
a ball rolling down an inclined plane is moving with
constant
acceleration

-

greater accelerations for steeper planes, max acceleration when
incline is tipped vertically

-

regardless of weight and size, when air resistance is small
enough to be neglected, all objects fall with the same unchanging
acceleration.

We call this acceleration the
acceleration due to gravity

on the Earth, and we give it the symbol
g.

g = 9.80 m/ s
2
~ 10 m/ s
2

How Far?

With his inclined planes Galileo found that the distance a
uniformly accelerating object travels is proportional to the
square of the time

Distance = acceleration x time x time /2.

It is common observation that many objects
fall with unequal accelerations: a leaf, a feather
or a sheet of paper may come to the ground
slowly. Why?

At a given location on the Earth and in the
absence of air resistance, all objects fall with the
same constant acceleration

A cat steps off a ledge and drops to the ground in ½ second.

(a)
What is its speed on striking the ground?

(b)
What is its average speed during the ½ second?

(c)
What is the height of this ledge?

1.
Which of the following (if any) could
not

be considered an
“accelerator” in an automobile: gas pedal, brake pedal,
steering wheel?

2.
A sports car accelerates from 65 mph to 75 mph in 2 seconds
while a minivan accelerates from 20 mph to 35 mph in 2
seconds. Which one has the larger acceleration?

3.
You are standing on a high cliff above the ocean. You drop a
pebble, and it strikes the water 4 seconds later. Ignoring the
effects of air resistance, how fast was the pebble traveling
just before striking the water? What is the height of the cliff?

Summary of Terms

Speed
: How fast something moves. The distance traveled per
unit time

Velocity
: The speed of an object and specification of its
direction of motion

Acceleration
: The rate at which velocity changes with time;
the change in velocity may be in magnitude or direction or
both.

Free fall

: Motion under the influence of gravity only.

Summary of Formulas

Speed = distance/time

Average speed = total distance covered/time interval

Acceleration = change of velocity/time interval

Acceleration (along a straight line) = change in speed/time interval

Velocity acquired in free fall, from rest:
v=gt

Distance fallen in free fall, from rest
:
d = gt
2
/2