Welcome to AP Physics C!

3-Ring Binder (with sections) Warm ups Notes Homework Quizzes and Tests Labs AP Reviews zAlso, yAP C Lab book yCalculator yFormula Cards

Definitions oParticle: oHas position, but not volume. oPosition of a particle: oA point; i.e. (x) or (x,y) or (x,y,z) oDistance: oLength of path traveled by particle. oDisplacement: oChange in position (  x = x 2 – x 1 )

A B 50 m displacement 100 m distance Distance vs Displacement

Average Speed s ave = d/t where: s is speed d is distance t is elapsed time

Average Velocity v ave = ∆x/ ∆t where: v ave is average velocity ∆x is displacement (x 2 -x 1 ) ∆ t is elapsed time (t 2 -t 1 )

Instantaneous velocity The velocity of a particle at an exact instant of time.

Average Velocity t x V ave =  x/  t, or the slope of the line connecting A and B. A B xx tt

Average Velocity t x V ave =  x/  t; still determined by the slope of the line connecting A and B. A B xx t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. a ave =  v/  t  v: change in velocity  t: 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) t0t0

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

Evaluating Derivatives If x = At n then v = dx/dt = (A)(n)t n-1

Instantaneous Acceleration Acceleration at a specific point in time. a = dv/dt dv/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)

Estimate the net displacement from 0 s to 4.0 s v (m/s) 2.0 t (s)

Kinematic Equations v = v o + at x = x o + v o t + ½ at 2 v 2 = v o 2 + 2a(x-x o )

Summary: Constant position graphs x t Position vs time v t Velocity vs time a t Acceleration vs time

Summary: Constant velocity graphs x t Position vs time v t Velocity vs time a t Acceleration vs time

Summary: Constant acceleration graphs x t Position vs time v t Velocity vs time a t Acceleration vs time

Basic equations v = v o + at x = x o + v o t + 1/2 at 2 v 2 = v o 2 + 2a(∆x)