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

• Acceleration is a vector quantity, but in 1D only need + or – to indicate direction

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

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.

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

• 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

• 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

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

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

2-8 Graphical Analysis of Linear Motion

• Displacement-time graphs

• Velocity-time graphs