3. ACCELERATIONVector quantity which measures how velocity changes over time Determined by the difference between the initial velocity (Vi) and final velocity (Vf) over change in time a ave = (vf – vi)/(tf –ti) = v/t Represented by the unit distance over time2 (ex) 12 m/s2 45 km/h2

4. Accelerating acceleration!?! For this class, we assume that all objects have constant acceleration. When an object accelerates, its displacement per unit time (velocity) changes.

5. ACCELERATION EQUATION a=Vf – ViVf = Vi + at Δt Where a = acceleration Vf = final velocity Vi = initial velocity Δ t = change in time

6. V f = V i + at Describes change in velocity under uniform acceleration. Tells how fast a particle will be going at time t if at time zero its velocity was v i. Converted to V f = at if V i = 0.

7. ACCELERATION PROBLEM Find average acceleration of a car that accelerates along straight road from rest to 80 km/h in 5 s. Vf = 80 km/h x h/3600s x 1000 m/km = 22.2 m/s Vi = 0 m/s a = (Vf – Vi)/ t = (22.2 m/s – 0 m/s)/5 s = 4.44 m/s 2

8. OBJECTS THAT ARE SLOWING DOWN Has negative acceleration (deceleration) Find average acceleration of a car moving to the right(+x direction) 15.0 m/s when the driver brakes to 5.0 m/s in 5.0 s? a =v/t = (5.0 m/s – 15.0 m/s) ÷ 5.0 s = -2.0 m/s2 (acceleration negative) Would acceleration still be negative if car was moving to the left? NO! Its acceleration would be directed to the right and be positive.

9. A shuttle bus slowed to a stop with an average acceleration of -1.8 m/s 2. How long did it take the bus to slow down from 9.0m/s to 0.0 m/s? a = -1.8 m/s 2 Vf = 0.0 m/sVi = 9.0m/s Δ t = ? Δt = Vf – Vi = (0.0 m/s – 9.0 m/s) =-9.0 m/s a-1.8 m/s 2 -1.8 m/s 2 a-1.8 m/s 2 -1.8 m/s 2 = 0.5 s `

10. A plane started from rest at one end of a runway underwent a uniform acceleration of 4.8 m/s 2 for 15.0s before take off. What was its speed at takeoff? a = 4.8 m/s2Δ t = 15.0 s Vi = 0.0 m/sVf = ? Vf=Vi + aΔt = 0.0 m/s + (4.8 m/s2)(15.0 s) = 72 m/s

11. Properties of acceleration In a velocity vs. time graph, the slope represents the object’s acceleration. In an acceleration vs. time graph, the area represents the object’s velocity.

12. Is negative acceleration slowing down? Not always Remember the (+) and (-) just tell us the direction of the quantity viviviviaMotion ++ Speeding up -- +- Slowing down -+ + or - 0 Constant speed 0 - or + Speeding up from rest 00 Remaining at rest

13. Determining time with constant acceleration and distance given What is the time needed by a car to travel 30 m while accelerating at 2.00 m/s2 from rest. x = ½ a t2 t2 = 2x/a t = (2x/a)1/2 t = (2(30m)/2.00 m/s2) = 5.48s a = 2.00m/s 2 x i = 0 v i = 0 x f = 30m

14. Free Fall Which falls faster: a feather or a hammer?

15. Galileo’s Experiment Which would reach the ground first, a marble or a cannonball?

16. Galileo’s Discovery In the absence of air resistance, all objects undergo equal acceleration as it falls to the earth. The value of acceleration due to gravity (g) is equal to: g = 9.80 m/s2

17. Kinematics Graph Position vs time graph (x or y vs. t) Slope is velocity Velocity vs time graph Slope is acceleration Area under graph is displacement Acceleration vs time graph Constant and non zero for uniform acceleration