1 Dimensional Motion
What you learned from you lab…
Objects moving at constant velocity
∆𝑥 = 𝑣𝑡
Objects accelerating
1 2
𝑥 = 𝑥𝑜 + 𝑣𝑜 𝑡 + 𝑎𝑡
2
𝑣 = 𝑣𝑜 + 𝑎𝑡
2
𝑣 =
2
𝑣𝑜
+ 2𝑎∆𝑥
Position, Distance, & Displacement
• Acknowledge your origin. Remember it might not be where you are
actually starting
• Position is where you are at an instant in time
• Distance is a scaler quantity and measures your total movement
• Displacement is a vector quantity that measures the straight line
distance between the starting position and the ending positon.
• This must have a magnitude and direction
The distance an objects travels is always
Greater than or equal to to its displacement
________________________
Below is the map of a person’s walk to school
• What is the total distance the person traveled?
• What is the magnitude and direction of the person’s displacement?
• If the person walked back home after school following the route in reverse,
what is the total distance traveled?
• What is the magnitude and direction of the person’s total displacement?
350m East in 2
minutes
400m North in
3 minutes
800m East in 5
minutes
Wait for your friend
for 2.5 minutes
Speed & Average Speed
• Speed is a scalar quantity that measures how fast you are moving.
• It is calculated using values that represent DISTANCE.
• Your average speed is calculated by taking your total distance and dividing
it by the total time it took to travel that distance.
• Stopping time is included in this calculation
1. If you travel 100 km at 20km/hr then travel 100km at 50km/hr,
• what is your overall average speed?
• Can you take the average of the two speeds?
28.6 km/hr
2. If you travel for 5 hours at 20km/hr then travel for 5 hours at 60km/hr,
• what is your overall average speed?
• Can you take the average of the two speeds?
40.0 km/hr
Is there a rule about calculating average speed?
Velocity, Average Velocity, & Instantaneous
Velocity
• Velocity is a vector quantity describing how fast you are moving.
• It is calculated using the value for DISPLACEMENT
• Your average velocity is calculated by taking your total displacement
and dividing it by the total time it took to travel that displacement.
• Stopping time is included in this calculation
• Your instantaneous velocity is your velocity at one instant in time.
1. Your average speed will always be __________________________
Greater than or equal to
your average velocity.
2. Can your instantaneous velocity be zero while your average
velocity is not? Explain.
Yes, when you turn around, you stop for a
second but still are moving overall
Below is the map of a person’s walk to school
• What is the average speed of the person? 124m/min
• What is the magnitude and direction of the person’s velocity? 97.4m/min @ 19.2o N of E
• If the person walked back home after school following the route in reverse,
but without stopping, what is the person’s average speed ON THE WAY
HOME? 155m/min
• What is the magnitude and direction of the person’s average velocity for
the entire day?
0 m/min
350m East in 2
minutes
400m North in
3 minutes
800m East in 5
minutes
Wait for your friend
for 2.5 minutes
Below is the position (m) vs. time (s) graph for an
object moving left and right. (right is considered
the positive direction)
10m
A
B
5
-7m
15
10
C
D
1. What is the overall average
1.2m/s
speed of the object?
2. What is the object’s total
-0.5m/s
average velocity?
3. How would you determine Find the slope
the instantaneous velocity of the tangent
of this object?
line
4. When is the instantaneous
Point B
velocity
of
the
object
the
20
greatest?
5. When is the instantaneous
A and C
velocity zero?
Acceleration
• The rate at which velocity is changing
• If the acceleration and velocity vectors are in the same direction, the object is
speeding up.
• If the acceleration and velocity vectors are in the opposite direction, the
object is slowing down.
1. Can an object be accelerating when its instantaneous velocity is
zero?
Yes, when its turning around
2. Can an object be accelerating when its speed is constant?
Yes, when its moving in a circle
Free Fall - Dropped
• An object in the air under the influence of Gravity only.
(air resistance is usually neglected)
• On Earth, the acceleration of an object in free fall is always
9.81m/s2 downwards throughout the entirety of the
motion.
• In this case it might be helpful to make the downward direction
positive so all your calculations do not end up with negative signs
• “dropped” implies vo is zero m/s
• All three acceleration formulas are valid.
• CAN NOT USE THE CONSTANT SPEED FORMULA FOR FREE FALL!
Thrown Downwards
• The object’s velocity will increase as it falls
• The initial velocity will be downwards (you can choose that to be
positive for ease)
• The acceleration is still 9.81m/s2 downwards
v
t
Thrown Upwards
• The initial velocity will be a positive value
v
t
• The acceleration must be negative
• The instantaneous velocity at the top of the motion is 0m/s
• The final velocity will be negative if its on the way down.
• The displacement is zero if the object is caught at the same height it
is thrown from.
• At this point, the magnitude of the downward velocity is equal in magnitude
to the initial upwards velocity.
• At any point below the initial release point, the magnitude of the object’s
velocity is greater than its initial velocity.
• The displacement is positive if the object is lands at a point higher
than its release
• The displacement is negative if the object is lands at a position lower
than it was thrown from.
Two objects Dropped Simultaneously
• Both have the same initial velocity
• Both have the same downward acceleration
-------------------------------------------------------------------------------• They must be moving at the same instantaneous velocity at
any point.
• They must have the same displacement at any given time.
• They will take the same amount of time to hit the floor.
The mass of the object does NOT affect its acceleration due
to gravity!
Practice
1. An object is dropped from a bridge 20m high
a. How long does it take to hit the water below?
b. What is its velocity when it hits the water?
2 seconds
19.8m/s
2. An object is thrown downwards off of a cliff at 7m/s. If the object hits the
ground 3 seconds later
65.1m
a. How high is the cliff?
b. How fast is it moving when it hits the ground?
36m/s
3. A coin is thrown upwards at 4.5m/s during a coin toss. If the coin is caught at
the same height it was released from,
a. What is the max height above the release point of the coin?
0.92s
b. How long is it in the air for?
c. What is the coin’s velocity when it is caught? 4.5m/s downwards
1.03m
4. A water balloon is thrown down from a window 12m above the ground. If the
water balloon hits the ground moving at 20m/s,
12.8m/s
a. How fast was it thrown out of the window?
It can be thrown up or down because it reaches that same
b. Was it thrown up or down? EXPLAIN
speed on the way down.
c. How long was it in the air for?
0.7 seconds
Two objects Dropped 1.0 Second Apart
dA (m)
vA (m/s)
4.9
9.81
Time Time
A (s) B (s)
dB (m)
vB (m/s)
1
19.6
19.6
2
1
44.1
29.4
3
2
78.5
39.2
4
3
122.6
49.1
5
4
4.9
9.81
19.6
19.6
44.1
29.4
78.5
39.2
Calculate the instantaneous
velocity and the displacement
of the object after each
interval of time.
1. What do you notice about
the difference in velocity
of A and B for each row?
It’s the same difference
every time
2. What to you notice about
their difference in positon
for each row.
Each second the objects are
farther apart
Position vs. Time Graphs
•
•
•
•
•
•
•
•
•
•
Y- value is the initial position
Above x-axis is positive position
Below x-axis is negative position
Slope is velocity
Positive slope is moving in the positive direction
Negative slope is moving in the negative direction
Horizontal line = standing still
Diagonal line = constant speed
Increasing slope = speeding up
Decreasing slope = slowing down
Velocity vs. Time Graphs
•
•
•
•
•
•
•
•
•
•
Y- value is the instantaneous velocity
Above x-axis is moving in the positive direction
Below x-axis is moving in the negative direction
Slope is acceleration
Area is displacement
Decreasing the magnitude of y-value means slowing down
Increasing the magnitude of y-value means speeding up
Horizontal line = constant speed
Diagonal line = accelerating
Line on x-axis = standing still
Acceleration vs. Time Graphs
• Y- value is the instantaneous acceleration
• Above x-axis is accelerating in the positive direction
• Below x-axis is accelerating in the negative direction
• Area is change in velocity
• Horizontal line = constant acceleration
• Diagonal line =changing accelerating
• Line on x-axis = constant velocity
Two Stage Motion
1. A racecar accelerates from rest for 5 seconds at a rate of 7m/s2 then
continues at a constant speed for an additional 20 seconds. How long is
the race?
787.5m
2. A child on a bicycle rides 300m at a constant speed of 7m/s then begins
to slows to a stop at a rate of 0.53m/s2.
a. How long does this take?
56.1 seconds
b. How far does the kid ride total
346.2m
3. A drive to a friend’s house takes 5 minutes. For the first 15 second, the
car accelerates out of the driveway and covers 130 meters. The car
maintains that constant speed of 4 minutes until it begins to slow to a
stop in the remaining time. How far away is your friend’s house?
4679.25 m
Two Object Motion
1. Two objects are dropped from a building 55m tall. They are
dropped 2 seconds apart.
2 seconds
a. How much time lapses between when they land?
13.2m/s
b. How fast is the second moving when the first hits the floor?
c. How far above the ground is the second when the first hits the floor? 46 m
2. Two objects are thrown from a window 18m high. The red one is
thrown up at 10m/s while the blue one is thrown downwards at
10m/s.
a. Which object is moving faster when they hit the ground below? Same speed
1.7 seconds
b. How much time lapses between when they land?
Two Object Motion
1. A cop sitting at rest on the side of the road sees a corvette speed by
at a constant 63m/s. The moment the corvette passes the cop, he
starts to accelerate at a uniform 1.3m/s2
a. How long does it take the cop to catch the corvette?
b. How far down the highway did he go?
6106m
96.6 seconds