Motion in One Dimension(Velocity vs.

Time)Chapter 5.2

What is instantaneous velocity?

What effect does an increase in velocity have on

displacement?

Instead of position vs. time, consider velocity

vs. time.

How can be determined from a v vs. t graph?

- Measure the under the curve.
- d vt
- Where
- t is the x component
- v is the y component

Measuring displacement from a velocity vs. time

graph.

What information does the slope of the velocity

vs. time curve provide?

- sloped curve velocity (Speeding

up). - sloped curve velocity (Slowing

down). - sloped curve velocity.

What is the significance of the slope of the

velocity vs. time curve?

- Since velocity is on the y-axis and time is on

the x-axis, it follows that the slope of the line

would be - Therefore, slope must equal .

Acceleration determined from the slope of the

curve.

What is the acceleration from t 0 to t 1.7

seconds?

Determining velocity from acceleration

- If acceleration is considered constant
- a ?__/?__ (__ __)/(__ __)
- Since ti is normally set to 0, this term can be

eliminated. - Rearranging terms to solve for vf results in
- __ __ a__

Velocity

Position, velocity and acceleration when t is

unknown.

- __ __ ½ (vf vi)t (1)
- vf vi at (2)
- Solve (2) for t t (__ __)/__ and substitute

back into (1) - df di ½ (vf vi)(__ __)/__
- By rearranging
- __ __ 2__(_____) (3)

Alternatively, If time and acceleration are

known, but the final velocity is not

- df di ½ (vf vi)t (1)
- vf vi at (2)
- Substitute (2) into (1) for vf
- df di ½ (__ __ __ __)t
- df di __ __ __ __ __ (4)

Formulas for Motion of Objects

Equations to use when an accelerating object has an initial velocity. Form to use when accelerating object starts from rest (vi 0).

?d ½ (vi vf) ?t ?d ½ vf ?t

vf vi a?t vf a?t

?d vi ?t ½ a(?t)2 ?d ½ a(?t)2

vf2 vi2 2a?d vf2 2a?d

Acceleration due to

- All falling bodies accelerate at the rate when

the effects of due to can be ignored. - Acceleration due to is caused by the

influences of Earths on objects. - The acceleration due to is given the special

symbol . - The acceleration due to is a to the

surface of the earth. - __/__

Example 1 Calculating Distance

- A stone is dropped from the top of a tall

building. After 3.00 seconds of free-fall, what

is the displacement, y of the stone?

Data Data

y ?

a g -9.81 m/s2

vf n/a

vi 0 m/s

t 3.00 s

Example 1 Calculating Distance

- From your reference table
- d ____ ____
- Since vi __ we will substitute __ for __ and __

for __ to get - __ ____

Example 2 Calculating Final Velocity

- What will the final velocity of the stone be?

Data Data

y -44.1 m

a g -9.81 m/s2

vf ?

vi 0 m/s

t 3.00 s

Example 2 Calculating Final Velocity

- Using your reference table
- vf __ __ __
- Again, since vi __ and substituting __ for __,

we get - vf __ __
- vf
- vf
- Or, we can also solve the problem with
- vf2 ___ _____, where vi __
- vf

Example 3 Determining the Maximum Height

- How high will the coin go?

Data Data

y ?

a g -9.81 m/s2

vf 0 m/s

vi 5.00 m/s

t ?

Example 3 Determining the Maximum Height

- Since we know the initial and final velocity as

well as the rate of acceleration we can use - ___ ___ ______
- Since ?__ ?__ we can algebraically rearrange

the terms to solve for ?__.

Example 4 Determining the Total Time in the Air

- How long will the coin be in the air?

Data Data

y 1.28 m

a g -9.81 m/s2

vf 0 m/s

vi 5.00 m/s

t ?

Example 4 Determining the Total Time in the Air

- Since we know the and velocity as well as

the rate of we can use - __ __ __ __, where __ __
- Solving for t gives us
- Since the coin travels both and , this value

must be to get a total time of s

Key Ideas

- Slope of a velocity vs. time graphs provides an

objects . - The area under the curve of a velocity vs. time

graph provides the objects . - Acceleration due to gravity is the for all

objects when the effects of due to wind,

water, etc can be ignored.

Important equations to know for uniform

acceleration.

- df di ½ (vi vf)t
- df di vit ½ at2
- vf2 vi2 2a(df di)
- vf vi at
- a ?v/?t (vf vi)/(tf ti)

Displacement when acceleration is constant.

Displacement area under the curve. ?d vit ½

(vf vi)t Simplifying ?d ½ (vf vi)t If

the initial position, di, is not 0, then df di

½ (vf vi)t By substituting vf vi at df

di ½ (vi at vi)t Simplifying df di

vit ½ at2