Acceleration

Physics 11

Acceleration

similar to how velocity is the rate of change of position w.r.t. time determined by the slope of a line on a position-time graph

acceleration is the rate of change of velocity w.r.t. time the slope of a line on a velocity-time graph

position time, velocity time and acceleration time graphs for a given situation are linked together

12

12

tt

vv

t

va

Acceleration

12

12

tt

vv

t

va

Graphing

Plot the following data in a position time graph

Determine the instantaneous velocity at t = 0.5 s, 2.0 s & 4.0 s

Use the data to plot a velocity time graph

Determine the slope of the line on the velocity time graph and use this to plot an acceleration time graph

Time (s) Position (cm)

0 2.0

0.5 3.2

1 6.9

1.5 13.0

2 21.6

2.5 32.7

3 46.1

3.5 62.1

4 80.5

4.5 101.3

5 124.6

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

0 1 2 3 4 5 6

Time (s)

Po

siti

on

(cm

)

0.0

10.0

20.0

30.0

40.0

50.0

60.0

0 1 2 3 4 5 6

Time (s)

Vel

ocity

(cm

/s)

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0 1 2 3 4 5 6

Time (s)

Acc

eler

atio

n (c

m/s

^2)

Examples of motion diagrams with position vectors:

An object is at constant or uniform speed if its displacement vectors are the same length.

Examples of motion diagrams with position vectors:

An object is slowing down if its displacement vectors are decreasing in length.

Examples of motion diagrams with position vectors:

An object is speeding up if its displacement vectors are increasing in length.

Examples of motion diagrams with velocity and acceleration vectors:

•For constant velocity, vectors are represented by the zero vector, , or a dot (no arrow).•Therefore, the acceleration vectors, , represented by the zero vector, , or a dot (no arrow). •This is no acceleration or constant velocity. The operational definition is the separation of position on a motion diagram remains constant in equal time intervals.

0

0

Examples of motion diagrams with velocity and acceleration vectors:

•For an object slowing down at a constant rate, the vectors are the same and point in the opposite direction to motion. Therefore, the acceleration vectors, , are the same length but point in the opposite direction to motion. •This is constant negative acceleration or slowing down in a positive direction. The operational definition of constant acceleration in this situation is the separation of position on a motion diagram decreases by the same amount in equal time intervals.

a

Examples of motion diagrams with velocity and acceleration vectors:

•For an object speeding up at a constant rate, the vectors are the same and point in the same direction as motion. Therefore, the acceleration vectors, , are the same length and point in the same direction as motion. •This is constant positive acceleration or speeding up in a positive direction. The operational definition of constant acceleration in this situation is the separation of position on a motion diagram increases by the same amount in equal time intervals.

a

For motion along a line:•An object is speeding up if and only if v and a point in the same direction.•An object is slowing down if and only if v and a point in the opposite direction.•An object’s velocity is constant if and only if a = 0.

•A positive or negative acceleration DOES NOT indicate that an object is speeding up or slowing down. •A positive acceleration can indicate a slowing down of an object in a negative direction OR a speeding up in a positive direction. •Conversely, a negative acceleration can indicate a speeding up of an object in a negative direction OR a slowing down in a positive direction.

Acceleration

Acceleration is a vector quantity the direction of both the velocity and acceleration is

crucial to understanding the situation Positive velocity with positive acceleration (faster to

the right/up) Positive velocity with negative acceleration (slower

to the right/up) Negative velocity with positive acceleration (slower

to the left/down) Negative velocity with negative acceleration (faster

to the left/down)

• Graphs are not pictures, but drawing pictures or pictorial representations that contain important information about a kinematics situation can provide a greater understanding of the motion. •The steps to drawing a pictorial representation are:

1. Draw a motion diagram.2. Establish coordinate system.3. Sketch the situation.4. Define symbols.5. List knowns and unknowns.6. Identify desired unknown.

Pictorial Representations

1.List known and unknown values and what value one wishes to find.

2.Draw a pictorial representation.3.Draw a motion diagram and graphical

representation (if appropriate).4.Develop a mathematical representation with

formulae using the variables and values in the pictorial representation. Solve.

5.Assess the result. Is the answer reasonable? Check for appropriate units and significant digits.

Problem-Solving Steps in Kinematics

Practice Problems

Page 42: #13

Use Figure 2-27 on page 42 to determine the average acceleration between t = 10 s & 30 s

Use Figure 2-27 on page 42 to determine the average acceleration between t = 70 s & 90 s