Acceleration And related topics: average velocity, instantaneous velocity, acceleration due to gravity.

AccelerationAnd related topics: average velocity, instantaneous velocity, acceleration due to gravity

Acceleration (a)

• Your concept of acceleration is probably lacking.• When the velocity of an object is changing it is

accelerating.• acceleration = rate of ∆ in velocity• Acceleration is the derivative of velocity as a

function of time. a = ∆v/∆t• Using physics variables, how would you write that

formula in calculus?

2 ways a body can accel.

• ∆ in mag. (speed up or slow down)• ∆ in direction (traveling in a curved path)

Annotation of velocity

• Initial velocity = vo or vi

• Final velocity = v or vf

•Other velocities = v1,v2,v3 ……

Average velocity

•When an object is accelerating we can not speak of velocity as we do when an object has constant velocity. We must speak in terms of average velocity during a time interval.•Acceleration is always implied.

Average velocity - formulas

• Vave = dt/tt

• Vave = (vf +vo)/2

• Vave = (v1 + v2 + v3 + … + vn)/n

Acceleration formulas - table 3-3 p.68•v = vo + at•d = vot + 1/2at2

•v2 = vo2 + 2ad

• Derivations• These are the forms of the equations I want you to use.

These are slightly different than those given in your text. Write these formulas on your formula note card.

Dimensions of acceleration

•MKS?•CGS?• Discuss what the dimensions mean.

Uniform acceleration

•Constantly changing velocity - magnitude or direction.

Instantaneous velocity

•Velocity @ one instant in time.•Define instant•Velocity for which the displacement is

measured over shorter & shorter time intervals.•Vins = vave over a short time interval

•Acceleration is always implied.

Vins cannot be measured w/ 100% accuracy• Since vins is only used with accel.

Motion, velocity is changing within an instant.•No matter how short the time interval

is a shorter time interval will yield a ∆ value of vins.

100% accuracy cont.

• Vins would be absolutely correct if it were so instantaneous that the displacement were meas. over the exact path. This would be impossible.• Either constant ∆ of direction or• ∆t = 0, then d/0 = undefined or ∆d = 0 the 0/0 =

0 and the object is obviously moving.• Therefore, vins cannot be meas. W/ 100%

accuracy.

More vins

• vave = vins only in the special case of constant v.•Vins can change in 2 ways: - ∆ speed - ∆ direction

Consider vins & 100% accuracy when direction not speed is changing

With circular motion speed is the limit of vins

vins & 100% accuracy cont.

• Therefore it is impossible to measure vins w/ 100% accuracy due to changes in either speed or direction.

• When direction is involved vins > vave

Instantaneous acceleration

•Also exist• Involves velocity & time instead of

displacement & time.

Acceleration due to gravity (g)• g = the accel. due to gravity. • g is a function of the mass of the body causing the accel..

Therefore since the mass of the earth is constant, g is also constant.

• g ≠ gravity. Gravity is the force that causes g and F ≠ a, although F a.

g• g = - 9.8 m/sec2 = - 980 cm/sec2 = -32 ft/sec2

Notice g is only in 2 sign. dig.

g formulas

• v = vo + at ---> v = vo + gt

• d = vot + 1/2at2 ----> d = vot + 1/2gt2

• v2 = vo2 + 2ad ----> v2 = vo

2 + 2gd

g exercise

• 1. Present the data from the handout in a data table.• 2. What general conclusion do you

draw from your data?• 3. From your data, hypothesize about

the value of g at sea level on the equator.• 4. What does the value of g at the N pole

compared to other locations tell you?• 5. Name a U.S. city with a N latitude of 45°.• 6. What is our approx. latitude?

Data table

Location & the value of g.

Location Value of g (m/s2)

N pole -9.832

Sea level @ 45o N latitude

-9.806

Denver -9.796