Motion in One Dimension
Jan 01, 2016
Motion in One Dimension
Kinematics Dynamics
Describes motion. The forces that cause motion.
Mechanics
Scalars and Vectors
There are two kinds of measurement: scalars and vectors.
Scalar – has only magnitude (size), such as distance. Ex. 35 m
Vector – has both magnitude and direction, such as position. Ex. 45 km north
Scalars (magnitude
only)Distance
Speed
MassTemperatur
eDensity
Vectors (magnitude
and direction)Displaceme
ntVelocity
Acceleration
Force
Momentum
A jet airplane travelled at 200km/hr towards the southwest. This is an example of a
Vector
Scalar
0%0%
1. Vector2. Scalar
200km/hr to the southwest represents …
Speed
Velocity
Dist
ance
Acceleration
Disp
lacement
0% 0% 0%0%0%
1. Speed2. Velocity3. Distance4. Acceleration5. Displacement
Position
Position (x) – the separation between an object and a reference point.
- it can be positive or negative depending on which side of the reference point that it is
Motion
Anytime an object changes its position (x), it is engaged in motion.
Displacement (Δx) = change in position
. Δx = xf - xi
xf = final position xi = initial position
Distance vs. Displacement
Joe Adams - punt returnDistance (d) = total amount travelled
regardless of direction (the real amount that Adams ran); scalar
Displacement (Δx) = the difference between the final and initial position (the yardage that shows up in the box score); vector
Reference Point
Reference point (or frame of reference) – a point that you label as zero and measure objects distance from
Average Velocity
Average Velocity
Average velocity = change in displacement per unit time
__ v = (xf–xi) / (tf–ti) = Δx/Δt = Δx/t
xf = position at clock reading t2
xi = pos. at earlier clock reading t1
∆x = xf – xi
∆t = t2 – t1
London Olympics and Average Velocity
Pure Speed
Usain Bolt and Average Velocity
In the water ...
Is Usain Bolt’s average velocity in the 200m greater, less, or the same as in the 100m?
Gre
ater in
the 200m
Less
in the 200m
The same in
the 200m (+
..
0% 0%0%
1. Greater in the 200m
2. Less in the 200m
3. The same in the 200m (+/- 1m/s)
Usain Bolt in the 200m
True or False: A car clocked with an average velocity of 85mph east must have been moving faster than a car clocked with an average velocity of 75mph east throughout
the entire time interval.
True
False
0%0%
1. True2. False
It is possible to have a negative velocity.
True
False
0%0%
1. True2. False
Acceleration
Acceleration – a vector quantity that describes the change in velocity over time
a = Δv/t
SI unit = m/s2
Position vs. Time Graphs
Slope = velocity
Straight line (constant slope) = constant velocity
Curved line = changing velocity = acceleration
Velocity-Time Graphs
Area underneath curve or line = displacement
Constant Slope ≠0 : constant acceleration
Zero slope = constant velocity
Acceleration Time Graphs
Used to visually show changes in acceleration.
Area under line = velocity
A velocity time graph with a slope of 0 is definitely not:
Moving
Accelerating
Moving back
war...
All of t
he abo...
0% 0%0%0%
1. Moving2. Accelerating3. Moving
backwards4. All of the above
A position time graph with a slope of 0 is definitely
Moving
Motionless
Accelerating
Moving back
war...
Exploding in
m...
0% 0% 0%0%0%
1. Moving2. Motionless3. Accelerating4. Moving
backwards5. Exploding in
midair
A position time graph that has is curving upward cannot be:
Moving in
the ...
Accelerating
Changing veloc...
At a nega
tive ...
At a co
nstant .
..
0% 0% 0%0%0%
1. Moving in the positive direction
2. Accelerating3. Changing
velocity4. At a negative
position5. At a constant
speed
A position time graph that is linear with a negative slope describes an object which is:
Motionless
Accelerating
Moving at
a co
...
All of t
he abo...
0% 0%0%0%
1. Motionless2. Accelerating3. Moving at a
constant velocity
4. All of the above
A velocity time graph that is linear could possibly describe an object which is:
Motionless
Accelerating
Moving at
a co
...
All of t
he abo...
0% 0%0%0%
1. Motionless2. Accelerating3. Moving at a
constant velocity
4. All of the above
The area between the line and the x-axis on a velocity time graph represents what?
Acceleration
Speed
Disp
lacement
Position
0% 0%0%0%
1. Acceleration2. Speed3. Displacement4. Position
The marble will finish first at the end of which color ramp? (Let the betting begin.)
Red
Gre
en
Yellow
Blue
All the sa
me
0% 0% 0%0%0%
1. Red2. Green 3. Yellow4. Blue5. All the same
The marble will complete the race with the least time on which color ramp?
Red
Gre
en
Yellow
Blue
All the sa
me
0% 0% 0%0%0%
1. Red2. Green 3. Yellow4. Blue5. All the same
Which ramp will the marble have the fastest average velocity? (Place your bets.)
Red
Gre
en
Yellow
Blue
All the sa
me
0% 0%
12%6%
82%1. Red2. Green 3. Yellow4. Blue5. All the same
Which color ramp will the marble have the smallest instantaneous velocity at the end of the ramp? (Place your bets.)
Red
Gre
en
Yellow
Blue
All the sa
me
14% 14%
0%
43%
29%
1. Red2. Green 3. Yellow4. Blue5. All the same
Which color ramp will the marble have the largest instantaneous velocity at the end of the ramp? (Place your bets.)
Red
Gre
en
Yellow
Blue
All the sa
me
0% 0% 0%0%0%
1. Red2. Green 3. Yellow4. Blue5. All the same
Types of Velocity
Constant velocity – this is a situation where the average velocity is the same for all time intervals.
Average velocity – takes into account the entire displacement and time; velocity may not always be constant
Instantaneous velocity – velocity at a given instant
Acceleration
Acceleration – a vector quantity that describes the change in velocity over time
a = Δv/t = (vf – vi)/t
SI unit = m/s2
Acceleration
A rocket ship has a negative acceleration but still seems to be speeding up. Is this possible? Justify your answer with concrete details backed up by data.
Acceleration Matrix
Initial Velocity Acceleration Type of Motion
+ + Speeding up
- - Speeding up
+ - Slowing down
- + Slowing down
+ or - 0 Constant velocity
0 + or - Speeding up from rest
0 0 Remains at rest
A car speeds up from 10 m/s south to 30 m/s south. Describe the acceleration.
Positive
Negative
Zero
Unable to
be d...
0% 0%0%0%
1. Positive2. Negative3. Zero4. Unable to be
determined
A cheetah slows down from 10 m/s south to 5 m/s south. Describe the acceleration.
Positive
Negative
Zero
Unable to
be d...
0% 0%0%0%
1. Positive2. Negative3. Zero4. Unable to be
determined
A minivan slows down from 85 mi/hr to 65 mi/hr when the driver spots a police officer tracking her speed. Describe her acceleration.
Positive
Negative
Zero
Unable to
be d...
0% 0%0%0%
1. Positive2. Negative3. Zero4. Unable to be
determined
An basketball is released from rest. When the ball hits the ground it is moving at a speed of 8m/s. Describe the acceleration.
Positive
Negative
Zero
Unable to
be d...
0% 0%0%0%
1. Positive2. Negative3. Zero4. Unable to be
determined
Tips for Solving Physics Problems
1) List all given information including unknown variable. Look for any inconsistent units (ex. cm and m/s) If all values are in SI units to start with, the final value will be an
SI unit.
2) List formulas that will be used to solve the problem (before plugging in data).
3) Plug in data and solve for unknown.
4) Box your answer and make sure the correct unit is present
EQUATIONS OF MOTION AT CONSTANT
ACCELERATION
Δx t vf vi a