One-Dimensional Motion

Experience vs. Experiment Through evolution and memory, humans have

developed a “sense” for motion Developed over years of observation, pattern recognition This understanding is qualitative (“general”, “vague”) No physics knowledge is required to catch a ball!

In physics, we aim to understand motion through experiment

Measure location of objects at specific times This understanding is quantitative (“specific”, “numerical”) With physics, if you know how the ball will be thrown, you

can predict where to stand to catch it!

Experience vs. Experiment – An Example

Identical balls race down two tracks

Which one will win the race?

Experience: Balls experience the same drop in height between

starting point and end point, so the race should be a tie Experiment:

Measure position of each ball every second Ball rolling on lowered track wins race!

Measurement of Motion: A Closer Look Question: “Where is the pen?”

Answer: “3 meters” (From where? In what direction?)

To measure a position in space, we must start with a reference point

Sometimes called the “origin” of a reference frame Position is relative; there is no universal origin

Motion is also relative Think of sitting in a train watching another train through

the window – tough to tell which is moving There is no universal “standing still”

Relative Motion Examples

The Earth Seems to be stationary in our experience Astronomy: Earth actually moves at about 60,000 mph in

orbit around the Sun Sun moves at about 500,000 mph in orbit around the

center of the Milky Way Galaxy Our experience misleads us once again!

Your car on the freeway Moving at 65 mph relative to road surface Moving at 5 mph relative to a car passing you Moving at 130 mph relative to a car driving on the other

side of the freeway

Speed

Speed measures how quickly an object moves Units: Examples: ,

mph

Instantaneous Speed: How fast an object is moving at a particular instant in time

Average Speed: How fast an object moves, on average, during a period of time

Equation:

An instantaneous speed can be thought of as an average speed for an infinitely short trip

Average Speed= total distance traveledtotal time elapsed

distancetime

metersseconds

Average Speed vs. Instantaneous Speed: An Example

The 100-meter dash The best in the world run the race in about 10 seconds

There are many instantaneous speeds during the race Are any of them larger than the average speed? Yes! The sprinter gets up to about 25 mph

Average Speed = total distancetotal time

= 100m10 s

= 10ms

= 22mph

v

t

10 sec5 sec

vaverage

vinstantaneous

Velocity

Velocity is defined as speed and direction 50 meters / sec is a speed 50 meters / sec to the east is a velocity

It is possible to change an object's velocity without changing its speed

Can you think of an example?

Acceleration

Acceleration is the rate of change of velocity (not speed!)

Ways to accelerate your car: Step on gas pedal (positive acceleration) Step on brake pedal (negative acceleration) Turn steering wheel (sideways acceleration)

Equation:

Units: Example:

acceleration = change of velocitytime elapsed

velocitytime

meters / secsec

ORmeters

sec2

Acceleration: Why is it useful?

Recall the work of Galileo and Newton The “natural state” of an object is constant velocity

By exerting forces on a system, we can change its state of motion

Forces change the system's velocity, causing acceleration

One-Dimensional Motion What is it?

Motion along a single line ( no turns or curves allowed ) Can move forward and/or backward along line Only need one number to measure position

Why is it important? Once we understand 1-D motion, we can apply the same

principles and equations to 2-D and 3-D motion

Examples:

Car on straight road Free fall Mass on spring

1-D Motion Experiment: Galileo's “Inclined Planes”

Observation: Ball gains speed as it rolls down incline

Hypothesis: The acceleration of the ball is constant for a given incline

Experimental Results: The ball's motion is consistent with constant acceleration

Galileo's Planes: Interpreting the Results

By measuring the distance traveled during each second, we can figure out the average speed during each second

If acceleration is constant, the average speeds will fit a pattern

v

t1 sec 2 sec 3 sec

Vaverage

(during 1st second)

Vaverage

(during 2nd second)

Vaverage

(during 3rd second)

Free Fall

If the only force acting on a physical system is gravity, the system is said to be in “free fall”

Let's ignore air resistance (for now)

Measurements show that objects in free fall accelerate at about 10 m/sec2

Regardless of their mass!

In physics, we use this so commonly that we give it a name:

Fgravity

g = 10m

sec2

Free Fall Experiment

Our experience tells us that heavy objects tend to fall faster than light objects

This is due to air resistance!

We can remove air resistance by dropping objects in a vacuum

Voila! Objects accelerate at same rate

Free Fall – Equations

Speed of free-falling object dropped from rest

Distance fallen by free-falling object

v = g tv = speed

t = time

g = 10msec2

d = 12g t 2