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2-4 Acceleration
• When the velocity of an object changes the object is accelerating.
• Average Acceleration is the change in velocity divided by the change in time
t
v
tt
vva
12
12
![Page 2: 2-4 Acceleration When the velocity of an object changes the object is accelerating. Average Acceleration is the change in velocity divided by the change](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649ee55503460f94bf4d93/html5/thumbnails/2.jpg)
• Acceleration is a vector quantity, but in 1D only need + or – to indicate direction
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Instantaneous Acceleration
• The acceleration at any instant, again where time approaches zero.
• Reminder that acceleration and velocity are not the same thing.
t
va
t
0
lim
![Page 4: 2-4 Acceleration When the velocity of an object changes the object is accelerating. Average Acceleration is the change in velocity divided by the change](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649ee55503460f94bf4d93/html5/thumbnails/4.jpg)
Deceleration
• Deceleration means that the object is slowing down
• But, a negative acceleration doesn’t always mean that the object is slowing down.
• Example???• There is deceleration when ever the
magnitude of the velocity is decreasing and then the velocity and acceleration point in opposite directions.
![Page 5: 2-4 Acceleration When the velocity of an object changes the object is accelerating. Average Acceleration is the change in velocity divided by the change](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649ee55503460f94bf4d93/html5/thumbnails/5.jpg)
2-5 Motion at Constant Acceleration
• To simplify; make initial time zero so then t2 = t (t2-t1=t)
• Initial values are not 1, but 0. (v1; v0 or x1; x0)
• Rearrange
t
vv
tt
vva 0
12
12
atvv 0
![Page 6: 2-4 Acceleration When the velocity of an object changes the object is accelerating. Average Acceleration is the change in velocity divided by the change](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649ee55503460f94bf4d93/html5/thumbnails/6.jpg)
• Rearrange
• Because acceleration is constant average velocity is between v and v0
• Combine
• Rearrange
t
xxv 0
tvxx 0
20 vv
v
tatvv
xtvv
xtvxx
2200
00
00
200 2
1attvxx
![Page 7: 2-4 Acceleration When the velocity of an object changes the object is accelerating. Average Acceleration is the change in velocity divided by the change](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649ee55503460f94bf4d93/html5/thumbnails/7.jpg)
• Begin with
• Solve for t
• Substituting into previous equation
• Solve for v2
atvv 0
a
vvt 0
a
vvx
a
vvvvxx
22
20
2
000
0
020
2 2 xxavv
tvv
xtvxx
2
000
![Page 8: 2-4 Acceleration When the velocity of an object changes the object is accelerating. Average Acceleration is the change in velocity divided by the change](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649ee55503460f94bf4d93/html5/thumbnails/8.jpg)
2-6 Solving Problems
• 1. Read and Reread• 2. What object(s) to study and what time interval• 3. Draw a diagram• 4. Write down known values (Watch Sig Figs)• 5. Plan of attack• 6. Equations to use• 7. Calculations• 8. Reasonable?• 9. Units
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2-7 Falling Objects
• At a given location all objects fall at the same constant acceleration. (In the absence of air resistance)
• Acceleration due to gravity
• 9.80 m/s2
• All equations are the same where a = g = 9.80 m/s2
![Page 10: 2-4 Acceleration When the velocity of an object changes the object is accelerating. Average Acceleration is the change in velocity divided by the change](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649ee55503460f94bf4d93/html5/thumbnails/10.jpg)
2-8 Graphical Analysis of Linear Motion
• Displacement-time graphs
• Velocity-time graphs