Unit 3, Uniform Acceleration Notes
Unit 3, Uniform Acceleration Notes
1. Find the instantaneous velocity at t = 2.0 s and t = 8.0s by finding slopes of tangents. To find the slope of the tangent I will find the slope of the secants lines where the mid-times are 2 and 8s. 2. Determine the average acceleration from t = 2.0s to t = 8.0s
βV = change in the instantaneous velocity (not the average velocity).
Notes v=
βπΏ
βπ a=
βπ
βπ
0,25
4,21
6, 16
10, 0 8 2
Physics Bell Work, Wednesday, Sept 30
2. Draw a motion map for the runner shown above showing that velocity is not constant but acceleration is uniform .
v v
v v v v
a a a a a
a
v
a
Ξt = 1s
Physics Bell Work, Wednesday, Sept
30
3. How are motion maps in questions 1 & 2 different? Map 1 is constant velocity (arrows same length, same dot spacing. Map 2 is increasing velocity (each arrow longer, dot spacing bigger).
Physics Bell Work, Monday, Feb 20
t (s) x (m)
0.0 4.0
2 10.0
4.0 16.0
6.0 22.0
8.0 28.0
10.0 34.0
4. Plot the data (draw the graph)
5. Calculate the slope 6. Determine the velocity. 5.
ππ π β π π
ππ π= π
π
π
6. Slope of an x-t graph = velocity, 3 m/s v = ππ β ππ
ππβππ
4
.
(s)
Worksheet
3, question
2
Bell Work Wednesday, 10/3/18 1. On a motion map how do we show an object is speeding up or slowing down? 2. Draw velocity and acceleration vectors that show an object that is speeding up and then slowing down to a stop at uniform acceleration.
Object speeding up
Object slowing down to a stop.
β’ When the objectβs acceleration vectors are in the same direction as its velocity vectors, the object is speeding up.
β’ When the vectors are in opposite directions, the object is slowing down.
v a
v
a
We must add an acceleration vector to the motion map.
1. A ball rolling up a ramp and the reversing direction and rolling down the ramp. Draw the motion map, velocity-time and acceleration-time graph that describes this motion.
0
v
a
v (
m/s
)
+
-
a (
m/s
2)
Time (s)
-
+ a
v
If an objectβs average acceleration during a time interval
is known, then it can be used to determine how much the
velocity changed during that time.
The definition of average acceleration:
Velocity with Average Acceleration
can be rewritten as follows:
Section 3.2-2
The equation for final velocity with average
acceleration can be written as follows:
Velocity with Average Acceleration
The final velocity is equal to the initial velocity
plus the product of the average acceleration and
time interval.
Section 3.2-3
In cases in which the acceleration is constant, the
average acceleration, Δ, is the same as the
instantaneous acceleration, a. The equation for
final velocity can be rewritten to find the time at
which an object with constant acceleration has a
given velocity.
It also can be used to calculate the initial velocity
of an object when both the velocity and the time at
which it occurred are given.
Velocity with Average Acceleration
Section 3.2-4
On the graph shown on the
right, v is the height of the
plotted line above the t-axis,
while Ξt is the width of the
shaded rectangle. The area of
the rectangle, then, is vΞt, or
Ξd. Thus, the area under the
v-t graph is equal to the
objectβs displacement.
Position with Constant Acceleration
Section 3.2-9
The area under the
v-t graph is equal to the
objectβs displacement.
Position with Constant Acceleration
Section 3.2-10
Finding the Displacement from a
v-t Graph
The v-t graph shows the
motion of an airplane. Find
the displacement of the
airplane at Ξt = 1.0 s and
at Ξt = 2.0 s.
Section 3.2-11
Are the units correct?
Displacement is measured in meters.
Do the signs make sense?
The positive sign agrees with the graph.
Is the magnitude realistic?
Moving a distance of about one football field in 2 s
is reasonable for an airplane.
Finding the Displacement from a
v-t Graph
Section 3.2-22
Section
3.1 Acceleration
Average acceleration is equal to the change in
velocity, divided by the time it takes to make that
change.
The following equation expresses average
acceleration as the slope of the velocity-time
graph.
Determining Acceleration from a v-
t Graph
Section 3.1-43
Section
3.1 Section Check
Which of the following statements correctly defines
acceleration?
Question 1
A. Acceleration is the rate of change of displacement of
an object.
B. Acceleration is the rate of change of velocity of an
object.
C. Acceleration is the amount of distance covered in
unit time.
D. Acceleration is the rate of change of speed of an
object.
Section 3.1-44
Section
3.1 Section Check
Answer 1
Reason: The rate at which an objectβs velocity
changes is called acceleration of the
object.
Section 3.1-45
Section
3.1 Section Check
What happens when the velocity vector and the
acceleration vector of an object in motion are in
the same direction?
Question 2
A. The acceleration of the object increases.
B. The speed of the object increases.
C. The object comes to rest.
D. The speed of the object decreases.
Section 3.1-46
Section
3.1 Section Check
Answer 2
Reason: When the velocity vector and the
acceleration vector of an object in
motion are in the same direction, the
speed of the object increases.
Section 3.1-47
Section
3.1 Section Check
On the basis of the
velocity-time graph of a
car moving up a hill, as
shown on the right,
determine the average
acceleration of the car?
Question 3
A. 0.5 m/s2
B. -0.5 m/s2
C. 2 m/s2
D. -2 m/s2
Section 3.1-48
Section
3.1 Section Check
Answer 3
Reason: Average acceleration of an object is
the slope of the velocity-time graph.
Section 3.1-49
Section
3.2 Motion with Constant Acceleration
If an objectβs average acceleration during a time interval
is known, then it can be used to determine how much the
velocity changed during that time.
The definition of average acceleration:
Velocity with Average Acceleration
can be rewritten as follows:
Section 3.2-2
Section
3.2 Motion with Constant Acceleration
The equation for final velocity with average
acceleration can be written as follows:
Velocity with Average Acceleration
The final velocity is equal to the initial velocity
plus the product of the average acceleration and
time interval.
Section 3.2-3
Section
3.2 Motion with Constant Acceleration
In cases in which the acceleration is constant, the
average acceleration, Δ, is the same as the
instantaneous acceleration, a. The equation for
final velocity can be rewritten to find the time at
which an object with constant acceleration has a
given velocity.
It also can be used to calculate the initial velocity
of an object when both the velocity and the time at
which it occurred are given.
Velocity with Average Acceleration
Section 3.2-4
Section
3.2 Motion with Constant Acceleration
The position data at
different time intervals
for a car with constant
acceleration are shown
in the table.
The data from the table
are graphed as shown
on the next slide.
Position with Constant Acceleration
Section 3.2-5
Section
3.2 Motion with Constant Acceleration
The graph shows that the
carβs motion is not uniform:
the displacements for equal
time intervals on the graph
get larger and larger.
The slope of a position-time
graph of a car moving with a
constant acceleration gets
steeper as time goes on.
Position with Constant Acceleration
Section 3.2-6
Section
3.2 Motion with Constant Acceleration
The slopes from the position
time graph can be used to
create a velocity-time graph
as shown on the right.
Note that the slopes shown
in the position-time graph
are the same as the
velocities graphed in the
velocity-time graph.
Position with Constant Acceleration
Section 3.2-7