9.1: Acceleration is the rate of change in velocity FRIDAY APRIL 25th APRIL (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 intervals  take different amounts of time to travel equal displacements  have a continuously changing velocity (c) McGraw Hill Ryerson 2007

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. (c) McGraw Hill Ryerson 2007

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

(c) McGraw Hill Ryerson 2007 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 Soccer players are continually changing their velocity.

Positive and Negative Changes in Velocity A change in velocity can be calculated by: (c) McGraw Hill Ryerson 2007

Positive change in velocity  If the change in velocity is the same sign (+, -) as the initial velocity, the speed of the object is increasing. (c) McGraw Hill Ryerson 2007

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? (c) McGraw Hill Ryerson 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. (c) McGraw Hill Ryerson 2007

Negative changes in velocity If the change in velocity is the opposite sign (+, -) of the initial velocity, the speed of the object is decreasing. (c) McGraw Hill Ryerson 2007

Example: Negative changes in velocity Now as you are cycling you apply the brakes to slow down. (c) McGraw Hill Ryerson 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 (c) McGraw Hill Ryerson 2007

Constant velocity If the change in velocity is zero, the object is travelling with uniform motion. (c) McGraw Hill Ryerson 2007

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. (c) McGraw Hill Ryerson 2007

Review (c) McGraw Hill Ryerson 2007 If forward is designated positive, this dragster’s change in velocity is positive.

(c) McGraw Hill Ryerson 2007 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 (c) McGraw Hill Ryerson 2007 Time (s)Velocity ( m/s) (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! (c) McGraw Hill Ryerson 2007

MONDAY APRIL 28thAPRIL (c) McGraw Hill Ryerson 2007

Colonel John Stapp ( ): Human acceleration 1940’s there was an emphasis on speed in transportation.  Jet planes speed reached 700 km/h  Grand prix race cars travelled at more then 150 km/h  Speed meant crashes that were usually fatal due to the large acceleration Colonel Stapp - pioneer in studying the effects of acceleration on the human body. (c) McGraw Hill Ryerson 2007

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. (c) McGraw Hill Ryerson 2007

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 min Motocross  Triathlon Triathlon 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. (c) McGraw Hill Ryerson 2007

Acceleration The fox needs to accelerate quickly and make rapid changes in velocity to catch the mouse. (c) McGraw Hill Ryerson 2007

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. (c) McGraw Hill Ryerson 2007

Example: (c) McGraw Hill Ryerson 2007 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. (c) McGraw Hill Ryerson 2007

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. (c) McGraw Hill Ryerson 2007

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

Examples of acceleration #1: (c) McGraw Hill Ryerson 2007 Acceleration is positive in this example accelerationvelocity 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 (+).

(c) McGraw Hill Ryerson 2007 Examples of acceleration #2: See pages Acceleration is negative in this example accelerationvelocity 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. (c) McGraw Hill Ryerson 2007

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

(c) McGraw Hill Ryerson 2007 A car speeds up in the backward direction.

This means that the acceleration is negative (-) even though the car is increasing its speed. Remember positive (+) and negative (-) refer to directions. (c) McGraw Hill Ryerson 2007

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

(c) McGraw Hill Ryerson 2007 A car slows down in the backward direction.

This means that the acceleration is positive (+) even though the car is decreasing its speed. Remember positive (+) and negative (-) refer to directions. (c) McGraw Hill Ryerson 2007

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? (c) McGraw Hill Ryerson 2007 A) The car’s change in velocity is 29 m/s [backward]. B) The direction of the car’s acceleration is backward.

Questions 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. (c) McGraw Hill Ryerson 2007 South There 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 (c) McGraw Hill Ryerson 2007 Take the Section 9.1 Quiz