Chapter 2
Motion in One Dimension
Homework Assignment
Active Figures:
12,13,15,22
Conceptual Questions
# 1,2,3,7,11,15
Problems
#,3,6,10,14,15,18,20,22,23, 24, 25,26, 28,30,32, 35,36,43,44,47,48,50
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
In kinematics, you are interested in the description of motion
Not concerned with the cause of the motion
Brief History of Motion
Sumaria and Egypt
Mainly motion of heavenly bodies
Greeks
Also to understand the motion of heavenly bodies
Systematic and detailed studies
"Modern" Ideas of Motion
Galileo
Made astronomical observations with a telescope
Experimental evidence for description of motion
Quantitative study of motion
Position
Vector Quantities
Vector quantities need both magnitude (size) and direction to completely describe them
Represented by an arrow, the length of the arrow is proportional to the magnitude of the vector
Head of the arrow represents the direction
Generally printed in bold face type
Scalar Quantities
Scalar quantities are completely described by magnitude only
Displacement
Measures the change in position
Represented as D x (if horizontal) or D y (if vertical)
Vector quantity
+ or - is generally sufficient to indicate direction for one-dimensional motion
Units are meters (m) in SI, centimeters (cm) in cgs or feet (ft) in US Customary
Displacements
Distance
Velocity
It takes time for an object to undergo a displacement
The average velocity is rate at which the displacement occurs
generally use a time interval, so let ti = 0
Velocity continued
Direction will be the same as the direction of the displacement (time interval is always positive)
+ or - is sufficient
Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust.)
Other units may be given in a problem, but generally will need to be converted to these
Speed
Speed is a scalar quantity
same units as velocity
total distance / total time
May be, but is not necessarily, the magnitude of the velocity
Instantaneous Velocity
The limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero
The instantaneous velocity indicates what is happening at every point of time
Uniform Velocity
Uniform velocity is constant velocity
The instantaneous velocities are always the same
All the instantaneous velocities will also equal the average velocity
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
Instantaneous velocity is the slope of the tangent to the curve at the time of interest
The instantaneous speed is the magnitude of the instantaneous velocity
Average Velocity
Instantaneous Velocity
Acceleration
Changing velocity (non-uniform) means an acceleration is present
Acceleration is the rate of change of the velocity
Units are m/s² (SI), cm/s² (cgs), and ft/s² (US Cust)
Average Acceleration
Vector quantity
When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasing
When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing
Instantaneous and Uniform Acceleration
The limit of the average acceleration as the time interval goes to zero
When the instantaneous accelerations are always the same, the acceleration will be uniform
The instantaneous accelerations will all be equal to the average acceleration
Graphical Interpretation of Acceleration
Average acceleration is the slope of the line connecting the initial and final velocities on a velocity-time graph
Instantaneous acceleration is the slope of the tangent to the curve of the velocity-time graph
Average Acceleration
Relationship Between Acceleration and Velocity
Uniform velocity (shown by red arrows maintaining the same size)
Acceleration equals zero
Relationship Between Velocity and Acceleration
Velocity and acceleration are in the same direction
Acceleration is uniform (blue arrows maintain the same length)
Velocity is increasing (red arrows are getting longer)
Relationship Between Velocity and Acceleration
Acceleration and velocity are in opposite directions
Acceleration is uniform (blue arrows maintain the same length)
Velocity is decreasing (red arrows are getting shorter)
Kinematic Equations
Used in situations with uniform acceleration
Notes on the equations
Gives displacement as a function of velocity and time
Notes on the equations
Shows velocity as a function of acceleration and time
Graphical Interpretation of the Equation
Notes on the equations
Gives displacement as a function of time, velocity and acceleration
Notes on the equations
Gives velocity as a function of acceleration and displacement
Problem-Solving Hints
Be sure all the units are consistent
Convert if necessary
Choose a coordinate system
Sketch the situation, labeling initial and final points, indicating a positive direction
Choose the appropriate kinematic equation
Check your results
Free Fall
All objects moving under the influence of only gravity are said to be in free fall
All objects falling near the earth’s surface fall with a constant acceleration
Galileo originated our present ideas about free fall from his inclined planes
The acceleration is called the acceleration due to gravity, and indicated by g
Acceleration due to Gravity
Symbolized by g
g = -9.8 m/s²
g is always directed downward
toward the center of the earth
Free Fall -- an object dropped
Initial velocity is zero
Let up be positive
Use the kinematic equations
Generally use y instead of x since vertical
Free Fall -- an object thrown downward
a = g
Initial velocity ¹ 0
With upward being positive, initial velocity will be negative
Free Fall -- object thrown upward
Initial velocity is upward, so positive
The instantaneous velocity at the maximum height is zero
a = g everywhere in the motion
g is always downward, negative
Thrown upward, cont.
The motion may be symmetrical
then tup = tdown
then vf = -vo
The motion may not be symmetrical
Break the motion into various parts
generally up and down
Non-symmetrical
Free Fall
Need to divide the motion into segments
Possibilities include
Upward and downward portions
The symmetrical portion back to the release point and then the non-symmetrical portion
Combination Motions
