CH 2: MOTION IN ONE
DIMENSION
DISPLACEMENT AND VELOCITY
• Displacement-The length of the straight line drawn
from your initial position to your final position as you
move from one position to another
• Change in position of an object
• Measured in meters
• Displacement does NOT equal distance traveled
DISPLACEMENT AND VELOCITY
Xi
Xf
DISPLACEMENT AND VELOCITY
• Displacement is an example of a quantity that has
both direction and magnitude
• In 1D motion there are only two directions in which
an object can move
• These can be specified by plus and minus signs
• Unless otherwise specified assume motion to the right is
positive and motion to the left is negative
• Similarly upward motion will be considered positive and
downward displacement will be considered negative
DISPLACEMENT AND VELOCITY
• The choice of right as positive and left as negative is
what is known as a convention
• Convention-is a system that is chosen for
convenience and consistency, not necessarily
because it has to be that way
• The convention can be reversed
DISPLACEMENT AND VELOCITY
• Velocity-The quantity that measures how fast
something moves from one point to another
• Has direction and magnitude
DISPLACEMENT AND VELOCITY
• To calculate the average velocity of an object you
must know the objects
• Displacement
• Time the object left its initial position
• Time the object arrived at its final position
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
=
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒
𝑡𝑖𝑚𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙
Average velocity=
𝑉𝑎𝑣𝑔 =
∆𝑥 𝑥𝑓 − 𝑥𝑖
=
∆𝑡
𝑡𝑓 − 𝑡𝑖
DISPLACEMENT AND VELOCITY
• Practice finding average velocity
• During a race on level ground, Andra covers 825 m
in 137 s while running due west. Find Andra’s
average velocity
• If you left your house at 10 A.M. and arrived at your
grandma’s house at 3 P.M. and your grandma’s
house is 370 km to the west , What was your
average velocity for the trip?
DISPLACEMENT AND VELOCITY
• The average velocity is equal to the constant
velocity you would need to have to cover the given
displacement in a given time interval
DISPLACEMENT AND VELOCITY
• In physics speed does NOT equal velocity
• Velocity has direction and magnitude, speed only
has magnitude
• Average velocity depends on the total
displacement
• Average speed is equal to the distance traveled
divided by the time interval
DISPLACEMENT AND VELOCITY
• When graphing velocity graph time vs. position
• The line connecting one point to another point
indicates the average velocity
• The slope of the line connecting the first point to the
last point equals the average velocity
• You can tell a lot about the velocity of an object by
the shape of its position-time graph
ACCELERATION
• Acceleration-the rate of change of velocity
• Calculated by dividing the total change in an
object’s velocity by the time interval in which the
change occurs
• 𝑎𝑎𝑣𝑔 =
∆𝑣
∆𝑡
=
• Units m/s2
𝑣𝑓 −𝑣𝑖
𝑡𝑓 −𝑡𝑖
ACCELERATION
• Acceleration has direction and magnitude
• When Δv is positive the acceleration is positive
• When velocity is constant, the acceleration is equal
to zero
• When something is slowing down the velocity is
positive, however, the acceleration is negative
• A negative value for acceleration can also occur
when an object is moving in the negative direction
and accelerating. This object decelerating would
have a positive value
ACCELERATION
vi
a
Motion
+
-
+
-
Speeding up
Speeding up
+
-
+
Slowing down
Slowing down
- Or +
0
0
- Or +
Constant velocity
Speeding up from rest
0
0
Remaining at rest
ACCELERATION
• Ball is fired with constant acceleration. A picture is
taken every tenth of a second
• Velocity increases by exactly the same amount
during each time interval
• Displacement for each time interval increases by the
same amount
ACCELERATION
• 𝑣𝑎𝑣𝑔 =
•
∆𝑥
∆𝑡
𝑣𝑖 +𝑣𝑓
2
= 𝑣𝑎𝑣𝑔 =
1
2
𝑣𝑖 +𝑣𝑓
2
• ∆𝑥 = (𝑣𝑖 + 𝑣𝑓 )∆𝑡
ACCELERATION
• A racing car reaches a speed of 4.2 m/s. It then
begins a uniform negative acceleration, using its
parachute and braking system, and comes to rest
5.5s later. Find how far the car moves while
stopping.
ACCELERATION
• 𝑎=
𝑣𝑓 −𝑣𝑖
∆𝑡
• 𝑣𝑓 = 𝑣𝑖 + 𝑎∆𝑡
• ∆𝑥 = 𝑣𝑖 ∆𝑡
1
+ 𝑎(∆𝑡)2
2
• This equation can also help find the distance
required for an object to reach a certain speed or
to come to a stop
ACCELERATION
• A plane starting at rest at one end of a runway
undergoes a constant acceleration of 4.8 m/s2 for
15 s before takeoff. What is its speed at takeoff?
How long must the runway be for the plane to be
able to take off?
ACCELERATION
• 𝑣𝑓 2 = 𝑣𝑖 2 + 2𝑎∆𝑥
• The square root of the right side of the equation
must be taken to find the final velocity
• The square root may be either positive or negative,
you must determine which is right
• Table 2-4 contains the equations that are used most
often
ACCELERATION
• A babysitter pushing a stroller starts from rest and
accelerates at a rate of 0.500 m/s2. What is the
velocity of the stroller after it has traveled 4.75 m?