1. Acceleration

2. Acceleration
As this guy skis, his velocity will go up or down as he descends or climbs hills.
His velocity will be changing; We say he accelerates.
Simply put: acceleration is how fast velocity changes.

3. Horizontal Acceleration

4. Understanding Acceleration and Its Units: m/s2
Car starts from rest
4 m/s
8 m/s
12m/s
16m/s
After 1 second
3 sec.
4 sec.
After 2 sec.
As each passes, the car’s increases by .
second
velocity
4m/s
Stated another way: the cars velocity increases by 4 m/s every second.
Its acceleration is 4- but what are the units?…

5. Understanding Acceleration and Its Units: m/s2
Stats from rest
8 m/s
12m/s
16m/s
4 m/s
After 2 sec.
3 sec.
4 sec.
After 1 second
It changes 4 m/s per second that passes; which can be written 4 m/s/s
In physics, this is always written as 4 m/s2.
d11Master Movie Video Clips\Physbcombocc down airtrack various inclines(02).vob

6. Variables used in Acceleration formulas
The following variables will be used:
a = acceleration (m/s2)- average acceleration
vi or v0 = initial velocity (m/s)- velocity with which it starts
vf = final velocity (m/s)- velocity with which it ends
t= time (s or sec)- time it takes for the velocity change to occur
d= displacement (m)- net distance over which the change of velocity takes place

7. Some Useful Acceleration formulas
4 main formulas
a = vf –vi/t
d= vit + ½ at2
vf2 = vi2 + 2ad
d = ½ (vf + vi)t
Variable not mentioned d vf t a
All of these may be manipulated to solve for the variable for which you are looking.

8. If a cheetah starts from rest and accelerates up to 30. 0 m/s in 5
If a cheetah starts from rest and accelerates up to m/s in 5.0 seconds, what was his average acceleration during this time?

9. If a cheetah stars from rest an accelerates up to 30. 0 m/s in 5
If a cheetah stars from rest an accelerates up to m/s in 5.0 seconds, what was his average acceleration during this hunt?
Knowns
vf = 30.0m/s
t= 5.0 sec.
vi=0 (starts from rest)
a= ? (unknown variable)
Which formula should be used?
To find out, determine which variable is not available/missing in this problem?
d (displacement)
Which is the only formula that can be used?
(To view formulas click here).
a = vf –vi/t
Confused about the missing variable verses unknown variable?
Click here.

10. If a cheetah stars from rest an accelerates up to 30. 0 m/s in 5
If a cheetah stars from rest an accelerates up to m/s in 5.0 second seconds, what was his average acceleration during this hunt?
Setup with numbers and units
a= 30.0 m/s- 0 m/s
5.0 sec
cal.= 6
Show original formula- then manipulate for the variable needed.
a = vf –vi t
Manipulate for variable needed
already solved for the variable needed- box original(a)
R =6.0 m/s2

11. Consider what the acceleration 6 m/s2 means:
Every second that passed the cheetah increased its speed by 6 m/s.
That is, 6 m/s per second, or 6 m/s2

12. Try another Acceleration problem
A dragonfly moves along the surface of a pond. It is traveling 16.0 m/s when it starts to slow down so it can land on a lily pad.
What was the acceleration of the dragonfly if it took 2.00 seconds to stop?

13. A dragonfly moves along the surface of a pond. It is traveling 16
A dragonfly moves along the surface of a pond. It is traveling 16.0 m/s when it starts to slow down so it can land on a lily pad. What was the acceleration of the dragonfly if it took 2.00 seconds to come to a stop?
Knowns
vi = 16.0m/s
t= 2.00 sec
vf=0 (slows to a stop)
a= ? (unknown variable)
Which formula is needed?
Which variable missing in this problem? d
Which is the only formula that can be used?
a= vf- vi/t

14. A dragonfly moves along the surface of a pond. It is traveling 16
A dragonfly moves along the surface of a pond. It is traveling 16.0 m/s when it starts to slow down so it can land on a lily pad. What was the acceleration of the dragonfly if it took 2.00 seconds to stop?
Original formula
a= Vf – Vi/t
Manipulate for (a)
Already solved for a
So box the original
Setup
a= 0 m/s – 16.0 m/s
2.00 sec.
Cal= -8
R= m/s2

15. Try another…
If the acceleration of the world’s fastest car is 20.0 m/s2, and it accelerates for 8.0 seconds- how far will it move from it’s starting point during this time?

16. If the acceleration of the world’s fastest car is 20
If the acceleration of the world’s fastest car is 20.0 m/s2, and it accelerates from rest for 8.0 seconds- how far will it move from it’s starting point during this time?
Knowns
a= 20.0 m/s2
t= 8.0 sec
vi=0 (from rest)
d= ?
Which formula is needed?
Missing variable? vf
Which formula can be used?
d= vit + ½ at2

17. d= (0 m/s)t + ½ at2 **d= ½ at2 d= vit + ½ at2
If the acceleration of the world’s fastest car is 20.0 m/s2, and it accelerates from rest for 8.0 seconds- how far will it move from it’s starting point during this time?
Show original formula
d= vit + ½ at2
Vi= 0 m/s
d= (0 m/s)t + ½ at2
**d= ½ at2
Because the initial velocity is zero, it shortens the formula before you start
**This step if used VERY often in physics when the initial velocity is zero.
Manipulation:
Not needed: box original formula

18. d= ½ at2 d= ½ (20.0 m/s2)(8.0sec)2 Cal= 640 R= 640 m
If the acceleration of the world’s fastest car is 20.0 m/s2, and it accelerates from rest for 8.0 seconds- how far will it move from it’s starting point during this time?
d= ½ at2
Setup
d= ½ (20.0 m/s2)(8.0sec)2
Cal= 640
R= 640 m

19. Another acceleration problem
A sailfish is swimming in place. How much time would it take it to accelerate at 4.0 m/s2 over a distance of 16.0 meters?

20. A sailfish is swimming in place
A sailfish is swimming in place. How much time would it take it to accelerate at 4.0 m/s2 over a distance of 16.0 meters?
Knowns
a= 4.0 m/s2
d= 16.0m
vi=0 (swimming in place)
t= ? (unknown variable)
Which formula is needed?
Missing variable? vf
Which is the only formula that can be used?
d= vit + ½ at2

21. d= (0 m/s)t + ½ at2 d= ½ at2 d= vit + ½ at2
A sailfish is swimming in place.How much time would it take it to accelerate at 4.0 m/s2 over a distance of 16.0 meters?
Show original formula
d= vit + ½ at2
This formula can be reduced.
d= (0 m/s)t + ½ at2
Because the initial velocity is zero, it is helpful to simplify the formula to…
d= ½ at2
This step is common.

22. d = t2 d= ½ at2 d = ½ at2 d = t2 ½ a ½ a d = t ½ a Original formula
A sailfish is swimming in place. How much time would it take it to accelerate at 4.0 m/s2 over a distance of 16.0 meters?
d = t2
½ a
Original formula
d= ½ at2
Manipulate for variable needed (t)
d = ½ at2
½ a ½ a
d = t2
½ a
d = t
½ a

23. A sailfish is swimming in place
A sailfish is swimming in place.How much time would it take it to accelerate at 4.0 m/s2 over a distance of 16.0 meters?
t = 2d a
Setup with numbers and units
t = m
4.0 m/s2
Don’t forget to square root!
cal.=
R= 2.8 sec

24. Would you like one more?
Yes No

25. A peregrine falcon constantly accelerates from 88 m/s to 32 m/s over a
distance of 30.0 meters.
How much time
would this take?

26. A peregrine falcon constantly accelerates from 88 m/s to 32 m/s over a distance of meters. How much time would this take?
Knowns
vi = 88 m/s
vf = 32m/s
d= 30.0 m
t= ? (unknown variable)
Missing variable? a
Which is the only formula that can be used?
(To view formulas click here).
d = ½ (vf + vi)t

27. A peregrine falcon constantly accelerates from 88 m/s to 32 m/s over a distance of meters. How much time would this take?
Show original formula
d = ½ (vf + vi)t
Manipulate for variable needed (t)
d = ½ (vf + vi)t
½ (vf + vi) ½ (vf + vi)
2d = t
(vf + vi)

28. A peregrine falcon constantly accelerates from 88 m/s to 32 m/s over a distance of meters. How much time would this take?
t = 2d
(vf + vi)
Is this positive or negative acceleration?
Negative.
Why isn’t the answer negative?
Time is always positive.
Setup with numbers and units
t = 2 (30.0m)
(32 m/s + 88m/s)
cal.= .5
R= .50 sec

29. Mini 2010 handed out problems from practice sheet

30. box R= with units! (5points)
For Today’s mini
Knowns with units!= (5 points)
Original and Boxed final manipulated formula= (5 points)
cal= (5 points)
Setup with units!= (5points)
box R= with units! (5points)

31. 1) How far will a car moving at a constant 12. 72 m/s go in 210
1) How far will a car moving at a constant m/s go in seconds?
Knowns 5pts
V= m/s
t= sec.
d= ?
Setup 5 pts
d= (12.72 m/s) (210.0 sec)
cal. = pts
R = 2671 m 5pts
Show original formula
v = d/t
5pts.
Boxed final formula
d=vt

32. 2) A dog on roller-skates starts from rest and accelerates at. 50 m/s2
2) A dog on roller-skates starts from rest and accelerates at .50 m/s2. He accelerates for a time of 8.4 seconds. What will the distance of the dog be during this time?
Knowns
a= .50 m/s2
t= 8.4 sec
vi=0 (from rest)
d= ?
5pts
Boxed final formula
d= ½ at2
Setup
d= ½ (.50 m/s2)(8.4 sec)2
5pts
5pts
Show original formula
d= vit + ½ at2
Vi= 0 m/s
d= (0 m/s)t + ½ at2
Cal= 17.64
5pts
R= 18 m
5pts

33. a = vf –vi/t t = vf –vi/a Setup 2.5 m/s2
3) How much time will it take a car accelerating at 2.5 m/s2 to go from 3.0 m/s to 8.0 m/s?
Knowns
a= 2.5 m/s2
vi= 3.0 m/s
vf= 8.0 m/s
t= ?
5pts
Boxed final formula
t = vf –vi/a
Setup
t= 8.0 m/s -3.0 m/s
Show original formula
a = vf –vi/t
5pts
5pts
2.5 m/s2
Cal= 2
5pts
R= 2.0 sec
5pts

34. d= (0 m/s)t + ½ at2 Setup a= 2 (100.0m) (4.5sec) 2 d= vit + ½ at2
4) A sports car at rest accelerates constantly for 4.5 seconds. During this time it moves meters. What is the acceleration?
Knowns
t= 4.5 sec
d= m
vi=0 (from rest)
a= ?
Boxed final formula
a= 2d t2
5pts
Setup a= 2 (100.0m) (4.5sec) 2
5pts
Show original formula
d= vit + ½ at2
Vi= 0 m/s
d= (0 m/s)t + ½ at2
5pts
Cal=
5pts
R= 9.9 m/s2
5pts

35. Older Acceleration/velocity mini no manipulation needed
Knowns with units!= (5 points)
Original and Boxed final manipulated formula= (5 points)
cal= (5 points)
Setup with units!= (5points)
box R= with units! (5points)

36. 1)How much time will it take car traveling a constant 22
1)How much time will it take car traveling a constant 22.5 m/s to move a distance of meters?
2) Starting from rest, a seal accelerates constantly at 1.5 m/s2 for 4.5 seconds. What distance will it cover during this time?
3) How much time would it take a go-cart at rest to accelerate at 4.0 m/s2 over a distance of 16.0 meters?
4) How much time will it take a car accelerating at 2.5 m/s2 to go from 3.0 m/s to 8.0 m/s?

37. 1) How much time will it take car constantly traveling 22
1) How much time will it take car constantly traveling 22.5 m/s to move a distance of meters?
Knowns 5pts
V= 22.5 m/s
d= m
t= ?
Setup 5 pts
t= (555.5 m)/(22.5 m/s)
cal. = pts
R = 24.7 sec. 5pts
Show original formula
v = d/t
Boxed final formula 5pts.
t=d/v

38. d= (0 m/s)t + ½ at2 Setup d= ½ at2 d= ½ (1.5 m/s2)(4.5 sec)2
2) Starting from rest, a seal accelerates constantly at 1.5 m/s2 for 4.5 seconds. What distance will it cover during this time?
Knowns
a= 1.5 m/s2
t= 4.5 sec
vi=0 (from rest)
d= ?
Boxed final formula
d= ½ at2
Setup
d= ½ (1.5 m/s2)(4.5 sec)2
Show original formula
d= vit + ½ at2
Vi= 0 m/s
d= (0 m/s)t + ½ at2
Cal=
R= 15 m

39. 3)How much time would it take a go-cart at rest to accelerate at 4
3)How much time would it take a go-cart at rest to accelerate at 4.0 m/s2 over a distance of 16.0 meters?
Setup with numbers and units
t = m
4.0 m/s2
Knowns
a= 4.0 m/s2
d= 16.0m
vi=0
t= ?
Don’t forget to square root!
cal.=
d= ½ at2
R= 2.8 sec
t = 2d a

40. Bellwork: warmup… date: (Acceleration)
[A coyote constantly accelerates from 4.00 m/s to m/s over a distance of 30.0 meters chasing a roadrunner. How much time would this take?]
Cal=
R= 2.67 sec

41. Which of the following would be a form of acceleration?-ask a neighbor
Slowing down
Making a left turn while speeding up
Making a right turn at a constant speed `
All OF THESE!
A change in speed or direction is a change of velocity= acceleration!

42. box R= with units! (5points)
For Today’s mini
Knowns with units!= (5 points)
Original and Boxed final manipulated formula= (5 points)
cal= (5 points)
Setup with units!= (5points)
box R= with units! (5points)

43. Bellwork: mini-quiz warm-up
John runs a certain distance in 4.5 seconds. If he is moving at 5.5 m/s, what is the distance (moving at a constant velocity)?
A bird starts from rest and accelerates at 4.5 m/s2 for over a distance of 26.0 m. How much time would this take?
For Today’s mini- practice these now.
Knowns with units!= (5 points)
Original and Boxed final manipulated formula= (5 points)
cal= (5 points)
Setup with units!= (5points)
boxed R= with units! (5points)

44. Bell work: Date:
Remember to write what is in brackets.[ ] and “Bellwork” and “date”.
[ What is the difference between speed and velocity?] Write two clear sentences to answer. 1)Speed is…. 2)Velocity is…

45. Bell work: Date:
Remember to write what is in brackets.[ ] and “Bellwork” and “date”.
[ Do you have all your materials today? How often will I be checking?]

46. Bell work: Date:
[A falcon lowers its velocity from 8.5 m/s to 4.3 m/s. It does this over 2.0 seconds of time. What is the acceleration of the bird of prey?]
Knowns
Original formula
Manipulated formula
Setup with units
Cal= R=
Cal= m/s2

47. Bell work: date:
[If a sled is sliding at 5.5 m/s and it comes to a stop over 4.0 seconds, what was it’s deceleration?]

48. Bell work: date:
[A skate boarder moving 3.5m/s takes a fall] trying to do a kick flip and ends up crashing [and he slides to a stop. If his deceleration was –1.5 m/s2, how long did it take him to stop?]
2.3 sec.