PHY 205 Ch2: Motion in 1 dimension 2.1 Displacement Velocity and Speed 2.2 Acceleration 2.3 Motion with Constant a 2.4 Integration Ch2: Motion in 1 dim.

2.1 Displacement, Velocity and Speed Ch2: Motion in 1 dim. Position, displacement, average velocity, speed defined: Choose axis, origin and direction. Assumption 1 dim space =real line

2.1 Displacement Velocity and Speed Ch2: Motion in 1 dim. Average velocity: graphical definition: Start with Position versus time graph for motion in ONE DIMENSION: Then, compute Displacement between t P and t Q : Then, Avg. velocity between t P and t Q : Position x Time t Graphically avg velocity = slope of secant PQ in x vs t graph Thus:

2.1 Displacement Velocity and Speed Ch2: Motion in 1 dim. Instantaneous velocity: graphical and algebraic definitions v x = Slope of tangent to graph x vs t at t P Thus, from that, we also get the graphical definition of v as:

2.2 AccelerationCh2: Motion in 1 dim. Graphical and algebraic definitions of acceleration (change of velocity with respect to time)

2.3 Motion with constant acceleration Ch2: Motion in 1 dim. If rusty with calc, just proceed backwards (not elegant but effective!) First lets assume a position X dependent on time as follows: Where A, B and C are constants) First avg velocity from generic t to t 1 =t+Δt: Same idea for acceleration from velocity, we get So for instantaneous we let Δt ->0 and get: Notice that constant A is 1/2a abd B=v(t=0) and C=x(t=0)

2.3 Motion with constant acceleration Ch2: Motion in 1 dim. So that for motion in 1 dim at constant acceleration a, we have the general equations : (these are the fundamental equations) – Make sure you understand meaning of all symbols! From the above equations we can derive (not fundamental) other equations: : Free fall: def. Constant downward acceleration g where g=9.81m/s 2 IF we take positive axis upward, and call position “y” then: note that g is NEVER negative – it’s just short hand for 9.81m/s 2 Note also: “top of trajectory” determined by: v y =0 “hits ground” determined by y=0 (if we take origin at ground level) but not v y =0 etc….

2.4 Integration Ch2: Motion in 1 dim. Taking derivatives from x (or antiderivatives from acceleration a ) we get