One Dimensional Motion
Motion in x or y only
Scalar vs. Vector

Scalar
Defined as quantity with magnitude (size) only
 Example: 3 m, 62 seconds, 4.2 miles
 EASY Math!!!


Vector
Defined as quantity with magnitude and direction
 Example: 3 m west, 62 seconds at 45º , 4.2 miles 
 Math is more complicated because you have to account for
the direction!!
 We use + and – to indicate direction!!!

Examples:
Label each as scalar or
vector:
 1. 6 m/s west
 2. 9.2 ft
 3. 82 kg
 4. 14 sec
 5. -19 m
 6. +6.2 mi/h
 7. 14.2 m at 30º

Distance vs. Displacement

Distance (d)

SI unit is meter (m)

Other units are ft, mile, etc,
but WE use metric only!
Scalar quantity, so math is
easy!!!
 Defined as “how far”
 Example: Jordan walks 5m
west then 15 meters east.
 What is her total distance?


Displacement (Δx, Δy)
SI unit is meter (m)
 Vector quantity, so direction
matters!
 Defined as straight-line
distance from end to start
 Example: Jordan walks 5m
west then 15 meters east.
 What is her total
displacement?

Speed vs. Velocity

Speed (s)



Defined as “how fast”
Calculated as
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑡𝑖𝑚𝑒
SI units are m/s
 Scalar quantity


𝑠=
𝑑
𝑡
Velocity (v)


Defined as “how fast and in
what direction”
Calculated as
𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑡𝑖𝑚𝑒
SI units are m/s
 Vector quantity


𝑣=
∆𝑥
𝑡
Example:

1. Splat the cat runs 21.2 m north, 16.5 m south, and 10.7 m north
again.
What is Splat’s total distance?
 What is Splat’s displacement?


2. A car notices mile marker 72 as it rolls east past it. The car
drives 68 miles east before turning around and speeding 16 miles
west. Calculate the car’s
Position
 Distance travelled
 Displacement

Average speed / velocity



We don’t “average” these the way you do other values!
𝑣𝑎𝑣𝑔 =
𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
𝑠𝑎𝑣𝑔 =
𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
Example: Allie drives 800 miles, from Texas to Florida. She
drives 90 mph for the first 100 miles. She gets busted and
slows to 20 mph for the remaining 700 miles.

1. How long did it take her to get to Florida?
TX to FL, continued……….


2. Calculate the average speed:
Whereas, if I just average the speeds, I get 55 mph! WAY
faster than Allie was going!!
Acceleration


Defined as rate of change in velocity
𝑎=
∆𝑣
∆𝑡
=
𝑣𝑓 −𝑣𝑖
∆𝑡
SI units are m/s2
 Vector quantity – has a direction

velocity
acceleration
Motion
+
+
Speeding up
+
-
Slowing down
-
-
Speeding up
-
+
Slowing down
Examples:

1. Splat the cat is running at 1.2 m/s when he speeds up to
3.7 m/s in 25.0 seconds. What is Splat’s acceleration?


2. Cassie sprints from rest to 6.5 m/s at a rate of 0.57 m/s2.
How long did it take Cassie to reach this speed?
Distance vs Displacement Graphs
Graph Example:






1. Find velocity for each segment.
2. Graph v vs. t for the motion.
3. Calculate the average velocity.
4. Graph the a vs. t for the motion.
5. What is the velocity and position at 5
seconds?
6. Describe how a person would walk
this graph.
Speed/Velocity Graphs
Graph Example:






1. Describe the motion of the graph.
2. What is the velocity, acceleration at
6 seconds?
3. Graph a vs t for this motion.
4. What is the total distance for the
graph?
5. What is the displacement for the
graph?
6. Graph d vs. t for this motion.
Acceleration graphs
Example:




1. Describe the motion of the graph.
2. What is the velocity change from 0
to .5 seconds?
3. What is the acceleration at 1.3 s ?
4. What final velocity at 1.5 seconds, if
initial velocity was 0 .
Constant Acceleration

Constant means “same”
Equation:
 𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡
2
2
 𝑣𝑓 = 𝑣𝑖 + 2𝑎∆𝑥



∆𝑥 = 𝑣𝑖 𝑡 +
∆𝑥 =
1
2
1
𝑎𝑡 2
2
𝑣𝑖 + 𝑣𝑓 𝑡
Use when this isn’t given:
x
t
𝑣𝑓
a
Example:

1. Splat begins from rest and accelerates to 8.7 m/s in 14.2
seconds.
What displacement did he travel?
 What was his acceleration?


2. When trying to bite me, Lucy the rabbit can move from
0.42 m/s to 4.9 m/s at a rate of 2.0 m/s2.
What distance did the rabbit travel?
 How long did it take the evil creature?

Freefall
All objects within earth’s atmosphere fall at the same rate of
𝑚
acceleration: 9.8 2 toward the surface
𝑠
 Same equations apply, but now I know “a” !!

Equation:
 𝑣𝑓 = 𝑣𝑖 − 𝑔𝑡
2
2
 𝑣𝑓 = 𝑣𝑖 − 2𝑔∆𝑥



∆𝑥 = 𝑣𝑖 𝑡 −
∆𝑥 =
1
2
1
𝑔𝑡 2
2
𝑣𝑖 + 𝑣𝑓 𝑡
Use when this isn’t given:
x
t
𝑣𝑓
a
Examples:

1. Lucy the rabbit falls from the top of a building. If it takes
her 1.92 seconds to fall to her demise, how tall was the
building?


1b. How fast does she hit the ground?
2. What if Lucy fell from a building on the moon, where
gravitational acceleration is only 1.6 m/s2 ? How long would
it take her to hit the ground from the same building?