1. Acceleration

2. Distance vs. Displacement
You drive the path, and your odometer goes up by 8 miles (your distance).
Your displacement is the shorter directed distance from start to stop (yellow arrow).
What if you drove in a circle?
start
stop

3. Speed
Speed is distance / time
or more accurately

4. Velocity is speed in
a given direction

5. Constant speed
A moving object that doesn’t change it’s speed travels at constant speed
Constant speed means equal distances are covered in an equal amount of time
What is the equation of the blue line?

6. What is the velocity at each point?
What is the average velocity?

7. m = m/s * sec
What is velocity?
m/sec = m/sec

8. What is average velocity?
m/sec = m/sec
What is average velocity?
for some interval
v = (df - di) / (tf – ti)

9. Average velocity: v = (df - di) / (tf – ti)
for some interval
v = (df - di) / (tf – ti)
What is Instantaneous velocity?
is made very small – infinitesimally small

10. What is happening to the velocity in this diagram?

11. Instantaneous velocity

12. Finding instantaneous velocity
Find the slope using small values of t and d.
Find the tangent to the line of d vs t.

13. Instantaneous velocity

14. Acceleration is a change in velocity over time.

15. Acceleration Acceleration is Acceleration is a VECTOR quantity
Units: Units of v is m/sec;units of t is sec
Units of a is m/sec2

16. Is there a meaning to the area under the line?

17. d = v t
The area under the curve is given by v * t.
The area under the curve is the distance.

18. Instantaneous and Average Velocity http://www. youtube. com/watch

19. Questions What if acceleration is in the same direction as velocity?
What if acceleration is in the opposite direction from velocity?

20. Equations  v = (df - di) / t vt = (df - di )  df = di + vt
 (vf – vi)/t = a
(vf – vi) = at  vf = vi + at
We usually ignore Dt = (tf – ti) and just use t since we can arbitrarily start the clock when we declare t=0

21. Examples
Asher is driving at 10m/sec (22 miles/hour) and accelerates at a rate of 1m/sec/sec (1m/sec2) for a period of 10 seconds.
What is Asher’s final velocity?
Sarah jumps out of an airplane. Her initial vertical velocity was 0 m/sec. Gravity accelerates a falling body at a rate of 9.8m/sec2 near the surface of the Earth. What is Sarah’s velocity after 5 seconds of free fall? What is this in mph?
If Sarah keeps falling for another 5 seconds, will her velocity double?
(Hint: Sarah is falling “spread-eagled”)

22. SAWITESU
Show All Work Including The EquationS and Units