9.1 Describing Acceleration

Review: What should we know already? So far, we have learned about uniform motion:  An object traveling with uniform motion has equal displacements in equal time intervals.  For uniform motion, we know how to describe:  Displacement  Distance  Velocity  Position

Non-Uniform Motion Not all objects have uniform motion. It is important to be able to analyze (look at) situations where the motion is not uniform. An object traveling with non-uniform motion will:  have different displacements during equal time intervals  take different amounts of time to travel equal displacements  have a continuously (always) changing velocity As she slides, the velocity of the baseball player is continually (always) changing, so her motion is non-uniform.

Changes in Velocity Remember, velocity is a VECTOR. Vectors have both direction (which way?) and magnitude (how much?) A change in velocity ( ) occurs when the speed of an object changes and/or its direction of motion changes. A change in velocity can be calculated by the following formula:

Reading + and – When we look at the + and – of change in velocity, it means:  The direction of the change  The size (magnitude) of the change in velocity If the change in velocity is the same sign (+, -) as the initial velocity, the speed of the object is increasing. If the change in velocity is the opposite sign (+, -) of the initial velocity, the speed of the object is decreasing. If the change in velocity is zero, the object is traveling with uniform motion. If forward is positive, this dragster’s change in velocity is positive. If forward is positive, this landing shuttle has a negative change in velocity.

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. 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. Both cars are starting from rest and speed up to 60 km/h. They will have the same change in velocity. Since the race car can get to 60 km/h faster than the old car, the race car will have a greater acceleration.

Positive Acceleration The direction of the acceleration is the same as the direction of the change in velocity. Examples of acceleration: 1. A car speeding up in the forward direction  If the forward direction is positive (+), then the change in velocity is positive (+), therefore the acceleration is positive (+).  (+) direction + (+) increase in magnitude = (+) acceleration A car going forward that speeds up has positive acceleration.

Negative Acceleration Examples of acceleration: 2. A car slowing down in the forward direction.  If the forward direction is positive (+), then the change in velocity is negative (-), therefore the acceleration is negative (-).  Acceleration that is opposite the direction of motion is sometimes called deceleration.  (+) direction + (-) decrease in magnitude) = (-) acceleration A car going forward slowing down has negative acceleration

Negative Acceleration due to direction Acceleration: 3. A car speeding up in the backward direction.  If we say the backward direction is negative (-) then the change in velocity is negative (-).  This means that the acceleration is negative (-) even though the car is increasing its speed.  (-) direction + (+) increase in magnitude) = (-) acceleration A car speeding up in the backward direction has negative acceleration.

Positive Acceleration due to direction Examples of acceleration: 4. A car slowing down in the backward direction.  If we say the backward direction is negative (-) then the change in velocity is positive (+).  This means that the acceleration is positive (+) even though the car is decreasing its speed.  (-) direction + (-) decrease in magnitude) = (+) acceleration A car slowing down in the backward direction has positive acceleration.

Summary ExampleDirection of MotionIncrease or Decrease in Speed Positive or Negative Acceleration Running to the dormitory because you forgot your homework (+) Positive (+) Increase (+) Positive Acceleration Slowly walking to the dormitory because you are tired (+) Positive (-) Decrease (-) Negative Acceleration (Deceleration) Quickly running to the cafeteria because you are hungry! (-) Negative (+) Increase (-) Negative Acceleration Slowly going to the cafeteria because you are not awake yet (-) Negative (-) Decrease (+) Positive Acceleration Cafeteria Dormitory (positive)