Unit B1.3 Acceleration

Types of Acceleration

Positive Acceleration Occurs in Two Ways– When an object’s velocity is increasing in a

positive direction. – When an object’s velocity is decreasing in a

negative direction

Negative Acceleration Occurs in Two Ways- When an object’s velocity is decreasing in a

positive direction- When an object’s velocity in increasing in a

negative direction

Using Formulas and Graphs to Analyze Accelerated Motion

Acceleration = change in velocity

time interval

a = vf - vi

∆t

Example

A racing car accelerates from rest to a speed of 200km/h (55.6m/s) [E] in 6.00s. What is the acceleration of the car.

Solution

a = vf - vi

∆t

a = 55.6m/s – 0.00m/s

6.00s

= 9.27m/s2

The car’s velocity is increasing at the rate of 9.27m/s2 [E] (This is positive acceleration)

Plotting a Position-Time Graph

Positive acceleration, slope is increasing.

Negative acceleration, slope is decreasing.

Example

Interpret the position-time graph for the data in the table

Using the graph, identify the motion occurring in the time intervals given below.i. Between 0.0s and 3.0s

ii. Between 3.0s and 6.0s

iii. Between 6.0s and 8.0s

Time (s) Position (m) [E]

0.0 0.0

1.0 10.0

2.0 40.0

3.0 90.0

4.0 140.0

5.0 190.0

6.0 240.0

7.0 270.0

8.0 290.0

Solution

0 1 2 3 4 5 6 7 8 90

50100150200250300350

Position as a Function of Time

Time (s)

Po

siti

on

(m

) [E

]

i. The curve has an increasing slope so it shows positive acceleration [E].

ii. The straight line shows uniform motion [E].

iii. The curve has a decreasing slope so it shows negative acceleration [E].

Practice Problem 16 p. 149

Plotting a Velocity-Time Graph

The slope of a velocity-time graph indicates the acceleration of the object.

slope = rise = ∆v

run ∆t

Example

Draw a velocity-time graph for the data shown in the table

Using the graph identify the motion occurring at the time intervals given below

i. Between 0.0s and 3.0s

ii. Between 3.0s and 5.0s

iii. Between 5.0s and 8.0s

Time (s) Velocity (m/s) [E]

0.0 0.0

1.0 2.0

2.0 4.0

3.0 6.0

4.0 6.0

5.0 6.0

6.0 4.0

7.0 2.0

8.0 0.0

Solution

0 1 2 3 4 5 6 7 8 901234567

Velocity as a Function of Time

Time (s)

Vel

oci

ty (

m/s

)

i. The straight line with a positive slope shows that the object was travelling with positive acceleration [E].

ii. The straight horizontal line shows uniform motion [E].

iii. The straight line with a negative slope shows negative acceleration [E].

Practice Problem 17 p. 153

i. CONVERTING km/h to m/s

Homework: read Science 10 p. 146 – 154 Practice Problems 12-17 pg 147-153 Check and Reflect 1-10 pg 154