Welcome to AP Physics C!

Mr. Smithsmithto@georgetownisd.org512-943-5100 x7066

3-Ring Binder (with sections)

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DefinitionsoParticle:

o Has position, but not volume.

oPosition of a particle:o A point; i.e. (x) or (x,y) or (x,y,z)

o Distance:o Length of path traveled by particle.

o Displacement:o Change in position (x = x2 – x1)

A

B

50 mdisplacement

100 m

distance

Distance vs Displacement

Average Speed

save = d/twhere:

s is speed

d is distance

t is elapsed time

Average Velocity

vave = ∆x/ ∆t

where:

vave is average velocity

∆x is displacement (x2-x1)

∆t is elapsed time (t2-t1)

Instantaneous velocity

The velocity of a particle at an exact instant of

time.

Average Velocity

t

x

Vave = x/t, or the slope of the line connecting A and B.

A

B

xt

Average Velocity

t

x

Vave = x/t; still determined by the slope of the line connecting A and B.

ABx

t

Instantaneous Velocity

t

x

Determined by the slope of the tangent to a curve at a single point.

B

Acceleration

•Speeding up

•Slowing down.

•Turning.

•Has magnitude and direction.

Average Acceleration

•Net change in velocity during time interval.

aave = v/tv: change in velocityt: change in time

Instantaneous Acceleration

oAcceleration at a particular instant of time

oSlope of tangent line to a velocity-time curve

Acceleration from Graph

t

v

Average acceleration is represented by the slope of a line connecting two points on a v/t graph.

Instantaneous acceleration is represented by the slope of a tangent to the curve on a v/t graph.

Acceleration from Graph

t

x

Instantaneous acceleration is negative where curve is concave down

Instantaneous acceleration is positive where curve is concave up

Instantaneous acceleration is zero where slope is constant

Instantaneous Velocity

Instantaneous velocity is the limit of x/t as t approaches zero.

v = lim (x/t)

t0

Instantaneous Velocity

v = dx/dtdx/dt is referred to as the derivative of position with respect to time.

Evaluating DerivativesIf

x = Atn

thenv = dx/dt = (A)(n)tn-

1

Instantaneous Acceleration

•Acceleration at a specific point in time.

a = dv/dtdv/dt is referred to as the derivative of velocity with respect to time.

Derivatives

•Slope of tangent line on graph

•x,t graph v

•v,t graph a

Integrals

•Area under curve on graph

•a,t graph v

•v,t graph x

Estimate the net change in velocity from 0 s to 4.0 s

a (m/s)

1.0

t (s)2.0 4.0

-1.0

Estimate the net displacement from 0 s to 4.0 s

v (m/s)

2.0

t (s)2.0 4.0

Kinematic Equations

•v = vo + at

•x = xo + vot + ½ at2

•v2 = vo2

+ 2a(x-xo)

Summary:Constant position graphs

x

t

Positionvs

time

v

t

Velocityvs

time

a

t

Accelerationvs

time

Summary:Constant velocity graphs

x

t

Positionvs

time

v

t

Velocityvs

time

a

t

Accelerationvs

time

Summary:Constant acceleration graphs

x

t

Positionvs

time

v

t

Velocityvs

time

a

t

Accelerationvs

time

Basic equations

v = vo + at

x = xo + vot + 1/2 at2

v2 = vo2 + 2a(∆x)