Name _________________________
AP Physics
Notes: Motion in One Dimension

Dynamics
- The branch of physics involving the motion of an object and the relationship
between that motion and other physics concepts.

Kinematics is a part of dynamics
o In kinematics, you are interested in the description of motion
o Not concerned with the cause of the motion
Quantities in Motion

Any motion involves three concepts
o Displacement
o Velocity
o Acceleration

These concepts can be used to study objects in motion
Brief History of Motion

Sumaria and Egypt
o Mainly motion of heavenly bodies

Greeks
o Also to understand the motion of heavenly bodies
o Systematic and detailed studies
o Geocentric model
“Modern” Ideas of Motion

Copernicus
o Developed the heliocentric system

Galileo
o Made astronomical observations with a telescope
o Experimental evidence for description of motion
o Quantitative study of motion
2.1 Displacement

Position - Defined in terms of a frame of reference
o One dimensional, so generally the x- or y-axis
o Defines a starting point for the motion

Displacement
o Defined as the change in position
o f stands for final and i stands for initial
o May be represented as y if vertical
o Units are meters (m) in SI, centimeters (cm) in cgs or feet (ft) in US Customary
Vector and Scalar Quantities

Vector quantities need both magnitude (size) and direction to completely describe them
o Generally denoted by boldfaced type and an arrow over the letter
o + or – sign is sufficient for this chapter

Scalar quantities are completely described by magnitude only

Displacement Isn’t Distance

The displacement of an object is not the same as the distance it travels
o Example: Throw a ball straight up and then catch it at the same point you released it
2.2 Velocity

The distance is twice the height

The displacement is zero

The average speed of an object is defined as the total distance traveled divided by the total time
elapsed
Average speed 
v 
total distance
total time
d
t

Speed is a scalar quantity

Average speed totally ignores any variations in the object’s actual motion during the trip

The total distance and the total time are all that is important

SI units are m/s
Example 2.1: A turtle and a rabbit engate in a footrace over a distance of 4.00 km. The rabbit runs
0.500 km and then stops for a 90,0 min nap. Upon awakening, he remembers the race and runs twice as
fast. Finishing the course in a total timew of 1.75 hours, the rabbit wins the race.
a. Calculate the average speed of the rabbit
b. What was his average speed before he stopped for a nap?

It takes time for an object to undergo a displacement

The average velocity is rate at which the displacement occurs
vaverage 
x xf  xi

t
tf  ti

generally use a time interval, so let ti = 0

Direction will be the same as the direction of the displacement (time interval is always positive)
o + or - is sufficient

Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust.)
o Other units may be given in a problem, but generally will need to be converted to these

Speed vs. Velocity
o Cars on both paths have the same
average velocity since they had the
same displacement in the same time
interval
o The car on the blue path will have a
greater average speed since the distance it traveled is larger
Graphical Interpretation of Velocity

Velocity can be determined from a position-time
graph

Average velocity equals the slope of the line joining
the initial and final positions

An object moving with a constant velocity will have a
graph that is a straight line

The straight line indicates constant velocity

The slope of the line is the value of the average
velocity

The motion is non-constant velocity

The average velocity is the slope of the blue line
joining two points
Instantaneous Velocity

The limit of the average velocity as the time
interval becomes infinitesimally short, or as the
time interval approaches zero
v  t lim0
x
t

The instantaneous velocity indicates what is happening at every point of time
Instantaneous Velocity on a Graph

The slope of the line tangent to the position-vs.-time graph is defined to be the instantaneous
velocity at that time
o The instantaneous speed is defined as the magnitude of the instantaneous velocity

Uniform velocity is constant velocity

The instantaneous velocities are always the same
o All the instantaneous velocities will also equal the average velocity

Example 2.2: Slowly moving train. A train moves slowly along a straight portion of track according to
the graph of position versus time in the figure.
a. Find the average velocity for the total trip,
b. Find the average velocity during he first 4.00 s of motion,
c. Find the average velocity during the next 4.00 s of motion,
d. Find the instantaneous velocity at t=2.00 s
e. Find the instantaneous velocity at t = 9.00 s.