2. Acceleration: a change in velocity!

3. What is Acceleration?? Sports announcers will occasionally say that a person is accelerating if he/she is moving fast. Yet acceleration has nothing to do with going fast. A person can be moving very fast, and still not be accelerating. Acceleration has to do with changing how fast an object is moving. If an object is not changing its velocity, then the object is not accelerating.

4. Acceleration Acceleration is a vector quantity which is defined as "the rate at which an object changes its velocity." (Speeding up or slowing down) An object is accelerating if it is changing its velocity (speed up or slow down). An object changing directions is changing its velocity so it is accelerating. An object at rest or at constant speed is NOT accelerating.

5. Acceleration Formula Units: m/s 2 a = ∆v ∆t (Can also be km/hr 2 - not common)

6. The analysis of a ticker tape diagram will also reveal if the object is moving with a constant velocity or accelerating. A changing distance between dots indicates a changing velocity and thus an acceleration. A constant distance between dots represents a constant velocity and therefore no acceleration.

7. The data at the right is representative of an accelerating object  the velocity is changing with respect to time. In fact, the velocity is changing by a constant amount change = 10 m/s in each second of time. So the object is accelerating at 10 m/s 2

8. Using the Acceleration Triangle ∆v a ∆t

9. Example 1: A motorbike starting from rest and undergoing uniform acceleration reaches a velocity of 20m/s (North) in 8.0 s. Find it’s average acceleration. a = Δ v Δ t Δ v = v f – v i = 20 – 0 = 20 Δ t = t f – t i = 8 – 0 = 8 a = (20 m/s N) (8.0 s – 0 s) = 2.5 m/s² North The motorbike’s average acceleration is 2.5 m/s² North.

10. Example 2 A racecar accelerates from rest at 10m/s 2 for 5 s. How fast, in m/s, will it be going at the end of that time?

11. Example 3 Gravity is the acceleration as you fall to earth of -9.8m/s 2. If you fall at this acceleration, how long will it take you to fall if you are going 22.3m/s?

12. Example 4 Use the table below to find the acceleration for this time interval. Time (min) Speed (m/min) 5.04.5 10.08.9 15.010.3 20.03.4 25.02.1

13. Use the equation for acceleration to determine the acceleration for the following two motions.

14. Practice A a = ∆v ∆t = 8 m/s – 0 m/s 4 s – 0 s = 2 m/s2

15. Practice B a = ∆v ∆t = 0 m/s – 8 m/s 4 s – 0 s = - 2 m/s 2

16. So, with positive velocity, we can have 3 graphs for velocity-time: tt t 1.No acceleration2. (+) acceleration3. (-) acceleration (speeding up) (slowing down) Positive directionPositive directionPositive direction Constant SpeedIncreasing SpeedDecreasing Speed

17. With negative velocity, we can also have 3 graphs for velocity-time: tt t 1.No acceleration2. (+) acceleration3. (-) acceleration (slowing down) (speeding up) Negative directionNegative directionNegative direction Constant SpeedDecreasing SpeedIncreasing Speed

18. Velocity vs. time graphs Consider a car moving with a constant, forward or right (+) velocity  say of +10 m/s. A car moving with a constant velocity is a car with zero acceleration (change in velocity).

19. Now consider a car moving with a forward (+), changing velocity  that is, a car that is moving rightward but speeding up or accelerating. Since the car is moving in the positive direction and speeding up, the car is said to have a positive acceleration.