Chapter 2
Section 1 - Displacement
1. The branch of physics that is concerned with the study of motion is called Dynamics
2. Straight line motion has 2 requirements
a. Displacement
b. Direction
3. Displacement – change in position
a. Straight line distance from initial to final position
i. SI = m or km
ii. Not always equal to distance traveled
b. Occurs along the x-axis in the coordinate system
i. use letter x to represent displacement
1.  x = change in displacement
2. xi = initial position
3. xf = final position
ii. x = xf - xi
c. Positive or negative.
i. If xi is greater than xf, your displacement is negative.
4. Velocity- the change in displacement over a given time
a. Measure how fast something is moving.
b. Average velocity - equal to displacement divided by time that it occurred.
c. SI = m/s
d. vavg = x = xf – xi
= displacement
 t = tf - ti
time interval
e. Velocity is not speed!
i. Velocity has magnitude and direction
1. based on DISPLACEMENT and time
ii. Speed has just magnitude
1. based on DISTANCE and time
f. (+) or (-) velocity
i. Sign indicates direction
g. Graphing velocity
i. Distance vs. time graph
1. slope shows average velocity = rise
run
2. Instantaneous velocity – velocity at an exact instant in time
a. Found by taking tangent to the position on the graph for a particular instance.
Section 2 - Acceleration
1. Acceleration – rate of change of velocity over a given time
a. (+) velocity = (+) acceleration
b. Constant velocity = 0 acceleration b/c no speeding up or slowing down
c. (-) acceleration if
i. vf < vi
d. Aavg = ∆v = vf - vi
∆t
t f - ti
e. SI = m/s2
f.
Practice Problem:
As a shuttle bus comes to a normal stop, it slows from 9.00 m/s to 0.00 m/s in 5.00 s. Find the
average acceleration of the bus.
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2. Motion with constant acceleration
a. Constant Acceleration - velocity increases by exactly the same amount during each time interval.
i. Pg 51 figure 2 – 11
ii. The time interval between each ball is 0.10 s.
1. As the velocity increases it travels a greater distance by exactly the same amount
during each time interval.
2. Because velocity increases by the same amount during each time interval:
a. displacement increases by the same amount during each time interval
3. THEREFORE, displacement w/ constant uniform acceleration
a. ∆x = ½ (vi + vf ) ∆t
(Manipulation of average velocity equation)
b. ∆x = vi ∆t + ½ a (∆t)2
b. Velocity w/ Constant Uniform Acceleration
i. vf = vi + a ∆t
c. Finding velocity if time is not known
i. vf2 = vi2 + 2a∆x
ii. Remember to take square root when necessary
3. Graphing Acceleration
a. Velocity vs. time graph
i. Average Acceleration = slope
ii. Instantaneous acceleration - ∆v at an instant in time
1. slope of line tangent at particular time
Section 3- Falling Objects
1. Freefall – falling toward the earth’s surface, undergoing the same constant acceleration.
a. (g) - constant acceleration due to gravity.
i. g = -9.81 m/s2 (981 m/s2 or 32 ft/s2)
ii. (-) b/c g is downward toward the center of the earth.
b. Tossing an object into the air
i. vi is in the (+) direction
ii. At its highest point v=0
iii. On way down, v will be (-).
1. Always have a (-) acceleration working against it.
c. Downward acceleration of freefalling bodies
i. (-) acceleration stays constant
1. Magnitude and direction of velocity changes
ii. Freefall equations
1. Same as other constant accel. equations
a. However, ∆x will then change to ∆y.
iii. Displacement from point of toss and back is technically zero.
1. Final displacement is (-) if falling the rest of the way to the ground.
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