Today Kinematics: Description of Motion Position and displacement velocity average instantaneous acceleration 09

Displacement Change in position from initial time to final time x (m) 4 3 -3

Velocity x(t) Which plot best represents v(t) t v(t) v(t) v(t) t t t Slope of x vs t gives v vs t Area under v vs t gives Dx! Which plot best represents v(t) 4s Dx Dt t 5s v(t) v(t) v(t) t t t

Acceleration (m/s2) v(t) t v(t) t The average acceleration is the change in velocity divided by the change in time. Instantaneous acceleration is limit of average velocity as Dt gets small. It is the slope of the v(t) plot v(t) Dt Dv t Give x vs t plot v(t) t 31

Position vs Time Plots Gives location at any time. Displacement is change in position. Slope gives velocity. x (m) t 4 3 -3 Position at t=3, x(3) = Displacement between t=1 and t=5. Dx = Average velocity between t=1 and t=5. v = 12

Velocity vs Time Plots Gives velocity at any time. v (m/s) Gives velocity at any time. Area gives displacement Slope gives acceleration. 3 1.5 6 t 4 velocity at t=2, v(2) = Change in v between t=3 and t=5. Dv = Average acceleration between t=3 and t=5: a = Displacement between t=0 and t=3: Dx= Average velocity between t=0 and t=3? v= -3 18

Acceleration vs Time Plots Gives acceleration at any time. Area gives change in velocity a (m/s2) 3 Acceleration at t=4, a(4) = Change in v between t=1 and t=4. Dv = t 4 t=1-3: Dv = -3 t=3-4: Dv = 21

Graphs

Graphs

Direction, Direction, Direction Velocity Acceleration Type of motion + + + - - - - +

Dropped Ball y x A ball is dropped from a height of two meters above the ground. Draw vy vs t -2 v t 4 3 A B C D E 34

Tossed Ball A ball is tossed from the ground up a height of two meters above the ground. And falls back down y x Draw v vs t v -2 t 4 3 A B C D E 42

Example: position vs. time Where is velocity zero? Where is velocity positive? Where is velocity negative? Where is speed largest? position vs. time Where is acceleration zero? Where is acceleration positive? 48

Example: velocity vs. time Where is velocity zero? Where is velocity positive? Where is velocity negative? Where is speed largest? velocity vs. time Where is acceleration zero? Where is acceleration positive?

Summary of Concepts kinematics: A description of motion position: your coordinates displacement: x = change of position velocity: rate of change of position average : x/t instantaneous: slope of x vs. t acceleration: rate of change of velocity average: v/t instantaneous: slope of v vs. t 50