9.1: acceleration is the rate of change in velocity friday april 25th april (c) mcgraw hill ryerson...

9.1: Acceleration is the rate of change in velocity

•FRIDAY APRIL 25th

(c) McGraw Hill Ryerson 2007


9.1 Describing Acceleration

•An object travelling with uniform motion has equal displacements in equal time intervals.

•Not all objects exhibit uniform motion.• It is important to be able to analyze

situations where the motion is not uniform.

See page 383

9.1: Non-Uniform Motion

•An object travelling with non-uniform motion will:have different displacements during equal

time intervalstake different amounts of time to travel

equal displacementshave a continuously changing velocity


Roller coaster

• You can feel the difference between motion that is nearly uniform and motion that is changing in speed and direction when riding a roller coaster.



As she slides, the velocity of the baseball player is continually changing, therefore her motion is non-uniform.


•What two aspects of motion can change when velocity changes?

• A change in velocity ( ) occurs when the speed of an object changes and/or its direction of motion changes.

See page 382

v

Soccer players are continually changing their velocity.

Positive and Negative Changes in Velocity

•A change in velocity can be calculated by:


v

v f

v i

Positive change in velocity

If the change in velocity is the same sign (+, -) as the initial velocity, the speed of the object is increasing.


Example: Positive change in velocity

• Suppose you are riding your bike forward at 6 m/s.• You speed up to 9 m/s forward.• How would you calculate your change in velocity?


6 m/s forward (+)

9 m/s forward (+)

Example: Positive change in velocity

• Positive ( + ) represents the forward direction in this example:

= +9 m/s – (+6 m/s)

= + 3• Therefore, the change in velocity is 3 m/s in the forward direction.

• You are speeding up by 3 m/s in the original direction.

• Your initial forward direction is positive, so your change in velocity is positive when you speed up.


v

v f

v i

Negative changes in velocity

•If the change in velocity is the opposite sign (+, -) of the initial velocity, the speed of the object is decreasing.


Example: Negative changes in velocity

• Now as you are cycling you apply the brakes to slow down.


9 m/s forward (+) 2 m/s forward (+)

Example: Negative changes in velocity

= + 2m/s – (+9m/s)

= - 7 m/s Your change in velocity is 7 m/s opposite the forward motion You are slowing down by 7 m/s in the original direction. Initial forward direction is (+) Your change in velocity is (-) when you slow down


v

v f

v i

Constant velocity

•If the change in velocity is zero, the object is travelling with uniform motion.


Example: Constant velocity

• You pedal at a constant velocity, your initial and final velocities would be equal.

• The change in velocity for that time interval would be zero.

• Any object travelling with uniform motion in a straight line would have zero change in velocity.


Review


If forward is designated positive, this dragster’s change in velocity is positive.


If forward is designated positive, this landing shuttle has a negative change in velocity.

Your turn.

• Question: Given the following data, calculate the change in velocity ( ) for the following time intervals. Let motion to the north represent positive (+) velocity.

a) 0 s – 5 s

b) 5 s – 10 s

c) 10 s – 15 s

d) 15 s – 20 s

e) 20 s – 25 s


v

Time (s) Velocity ( m/s)

0 0

5 8

10 12

15 12

20 15

25 9

(e) –6 m/s; 6 m/s [S]

(a) +8 m/s; 8 m/s [N]

(b) +4 m/s; 4 m/s [N]

(c) 0 m/s

(d) +3 m/s; 3 m/s [N]

To be continued!


•MONDAY APRIL 28th


Colonel John Stapp (1910-1999): Human acceleration

• 1940’s there was an emphasis on speed in transportation.Jet planes speed reached 700 km/hGrand prix race cars travelled at more then 150

km/hSpeed meant crashes that were usually fatal

due to the large acceleration

•Colonel Stapp - pioneer in studying the effects of acceleration on the human body.


•Stapp: called the “fastest man on Earth”.Did his research at Edwards Air Force Base in

California

• 1947: Scientists didn’t have any computers or crash-test dummies to use to analyze accelerations on humans.

•Stapp used himself in his acceleration experiments.


•Discovered that humans could survive 46 g (the symbol for the value of the acceleration due to gravity|) not die at 18 g as thought.Seat belts today are a result of Stapp’s

research.

•Discovered humans can withstand a larger acceleration when riding backward.Result, infant seats in cars are made to face

backward.(c) McGraw Hill Ryerson 2007


Acceleration

•Acceleration (a) is the rate of change in velocity.This change in velocity can be due to a

change in speed and/or a change in direction or both.

Motocross clip start 3:45 minTriathlon - 2010

See page 384

Acceleration

•When we talk about acceleration, we need to include:The magnitude of the change in the

velocity of the moving object.To indicate the change in direction of the

object’s velocity.


Acceleration

• The fox needs to accelerate quickly and make rapid changes in velocity to catch the mouse.


Comparing Acceleration

•Two objects with the same change in velocity can have different accelerations.This is because acceleration describes the

rate at which the change in velocity occurs.


Example:


• Suppose both of these vehicles, starting from rest, speed up to 60 km/h.

• They will have the same change in velocity, but, since the dragster can get to 60 km/h faster than the old car, the dragster will have a greater acceleration.

Learning check.

•Question: How can you tell which of two objects has the greater acceleration?

•Answer: The object with the greater acceleration changes its velocity in a shorter time interval or has a greater change in velocity during the same time interval.


Positive and negative acceleration

•When you think of acceleration, you probably think of something speeding up.

•However, an object that is slowing down is also changing its velocity, and is accelerating.

• In straight-line motion, acceleration can be either positive or negative.



Positive and Negative Acceleration

• The direction of the acceleration is the same as the direction of the change in velocity.

• Acceleration that is opposite the direction of motion is sometimes called deceleration.

See pages 385 - 386

Examples of acceleration #1:


Acceleration is positive in this

example

1. Tin Tin is speeding up in the forward direction If we designate the forward direction as positive

(+), then the change in velocity is positive (+), therefore the acceleration is positive (+).


Examples of acceleration #2:

See pages 385 - 386

Acceleration is negative in this example

2. Tin Tin is slowing down in the forward direction. If we designate the forward direction as positive

(+), then the change in velocity is negative (-), therefore the acceleration is negative (-).

Direction

•Positive ( + ) and negative ( - ) acceleration are also dependent upon the direction of an object’s motion.



Examples of acceleration #3 with direction:

3. A car speeding up in the backward direction. If we designate the backward direction as

negative (-) then the change in velocity is negative (-).

See pages 385 - 386


• A car speeds up in the backward direction.

vvv f

m/s1m/s4 backwardsm/s3m/s3

• This means that the acceleration is negative (-) even though the car is increasing its speed. Remember positive (+) and negative (-) refer to directions.



Example of acceleration # 4 with direction:

4. A car slowing down in the backward direction. If we designate the backward direction

as negative (-) then the change in velocity is positive (+).

See pages 385 - 386

v f 1m/s

v i 4m/s


forwardm/s3

v f 1m/s

v i 4m/s

A car slows down in the backward direction.

m/s4m/s1 if vvv

• This means that the acceleration is positive (+) even though the car is decreasing its speed. Remember positive (+) and negative (-) refer to directions.


v f 1m/s

v i 4m/s

forwardm/s3

Your turn

1) A car travelling forward at 25.0 m/s stops and backs up at 4.0 m/s.

A) What is the car’s change in velocity?

B) What is the direction of the car’s acceleration?


A) The car’s change in velocity is 29 m/s [backward].

B) The direction of the car’s acceleration is backward.

Questions 9.1

2. Suppose a motorcycle’s change in velocity is 15 m/s [S]. What is the direction of the motorcycle’s acceleration?

3. A tennis ball, initially travelling at 20 m/s, is hit by a racket at 20 m/s. Explain how there is a change in velocity even though the initial and final speed of the ball is the same.


SouthThere is a change in velocity because the tennis ball is travelling in different directions. One of the directions would be represented by a positive (+) sign while the other direction is represented by a negative sign (-).

•The End of 9.1


Take the Section 9.1 Quiz

9.1: acceleration is the rate of change in velocity friday april 25th april (c) mcgraw hill ryerson...

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