http://geocities.com/kenahn7/ Today in this class Chap.2, Sec.1-7 Motion along a straight line 1. Position and displacement 2. 3. Acceleration Example: Motion with a constant acceleration

Position and displacement Motion A lot of things move! Motion One of the main topics in Physics 105 Let s start with the simplest kind of motions. Motion along a straight line (title for Ch.2) (i.e., 1-dimensional motion) Position and displacement Straight line Straight line can be oriented along any direction: Horizontal, vertical, or at some angle

Position and displacement Position What is motion? Change of position over time How to represent position along a straight line: define: x 0 some position (Origin) positive direction for x length unit, e.g., meter Position of ball: x +3 m Position and displacement Concept of vector Vector: Quantity with both magnitude and direction (Ex) Position, Displacement, Velocity, Acceleration : Vectors Mass : Not vector For the motion along a straight line (1-dimensional case) the direction is represented simply by + and - signs Vectors in plane(2d) or space(3d) : Ch.3, next lecture

Position and displacement Displacement Displacement : Change in position x 2-2 m x 1 +3 m (Displacement) x -5 m + or sign represents direction Length unit, e.g., meter x(t) : position as a function of time Define time : t0 and time unit, e.g., second x 0 x 2 m t (s) x (m) x -6 m

Average velocity, v avg (Average velocity between time t 1 and t 2 ) v avg x( t ) x( t ) x x Ex.) 2 1 2 1 t2 t1 t2 t1 x 4.4 m 1.6 m 6.0 m t 8.0 s 2.0 s 6.0 s v avg x 6.0m 1.0 m/ s t 6.0s x t Unit : [Length]/[Time], e.g., m/s (Displacement) Average velocity, v avg (Average velocity between time t 1 and t 2 ) v avg x( t ) x( t ) x x Ex.) 2 1 2 1 t2 t1 t2 t1 x 4.4 m 1.6 m 6.0 m t 8.0 s 2.0 s 6.0 s v avg x 6.0m 1.0 m/ s t 6.0s Slope of the green line x t (Displacement)

Average speed, s avg (Average speed between time t 1 and t 2 ) s avg (Total distance) Distance & s avg : always positive, no direction Not a vector In general, Average speed Average velocity Example: X0 km x 50 km t 0 min Average speed, s avg (Average speed between time t 1 and t 2 ) s avg (Total distance) Distance & s avg : always positive, no direction Not a vector In general, Average speed Average velocity Example: X0 km x 50 km t 50 min

Average speed, s avg (Average speed between time t 1 and t 2 ) s avg (Total distance) Distance & s avg : always positive, no direction Not a vector In general, Average speed Average velocity Example: X0 km x 50 km t 50 min Average speed, s avg (Average speed between time t 1 and t 2 ) s avg (Total distance) Distance & s avg : always positive, no direction Not a vector In general, Average speed Average velocity Example: X0 km x 50 km t 100 min

Average speed, s avg (Average speed between time t 1 and t 2 ) s avg (Total distance) Distance & s avg : always positive, no direction Not a vector In general, Average speed Average velocity Example: Between t0 and 100 min (Total displacement)0, (Avg. velocity)0 X0 km x 50 km t 100 min Average speed, s avg (Average speed between time t 1 and t 2 ) s avg (Total distance) Distance & s avg : always positive, no direction Not a vector In general, Average speed Average velocity Example: Between t0 and 100 min (Total distance)100 km, (Avg. speed)1 km/min X0 km x 50 km t 100 min

Instantaneous velocity, or velocity How fast at a given time t Instantaneous velocity, or simply, velocity x( t+ t) x( t) dx vt () lim t dt t 0 Vector with + or - sign Slope of tangential line at t in x vs. t curve Rate of change in position Velocity from x vs. t curve Example: Elevator Position (m) Time (s) Velocity (m/s) Time (s)

Speed Speed : Magnitude of velocity Example: Speedometer of your car speed, not velocity Acceleration Average acceleration, a avg Instantaneous acceleration(or acceleration), a (Average acceleration between time t 1 and t 2 ) a avg vt ( 2) vt ( 1) v2 v1 v t t t t t 2 1 2 1 (Velocity change) Instantaneous acceleration (or acceleration) at time t vt ( + t) vt ( ) dv at () lim t dt t 0 Unit: (m/s)/sm/s 2 : [Length]/[Time] 2 + or sign : direction vector 2 d dx d x dt dt 2 dt

Acceleration Acceleration from v vs. t curve Example: Elevator Acceleration (slope of tangential line in v vs. t curve) Velocity (m/s) Acceleration (m/s 2 ) Time (s) Example: Motion with a constant acceleration Very common! Free fall of objects : a-9.8 m/s 2, when + means upward. Acceleration of a stopped car or elevator until it reaches constant velocity : Approximately, constant. Deceleration of a moving car or elevator until it stops : Approximately, constant.

Motion with a constant acceleration Example of x vs. t v vs. t a vs. t graphs x t v t a t Example: Motion with a constant acceleration General form of a(t), v(t), x(t) Given : a(t)constanta v(t0)v 0, x(t0)x 0 Initial condition vt () v a a 0 avg vt () v t 0 0 at v v0 + a t x() t x v 0 avg xt () x t 0 0 vavg t x x0 + vavg t Since velocity changes at a constant rate, vavg ( v+ v0 )/2 v v0 ( v0 at) v0 2v0 at x x + 0 t x + + 0 t x + + 0 t 2 + + 2 2 1 2 x x0 + v0t+ at 2

Example: Motion with a constant acceleration Relations between x and v Given : a(t)constanta v(t0)v 0, x(t)x 0 Initial condition a a avg vt () v t 0 0 v v0 ( v0 at) v0 2v0 at x x + 0 t x + + 0 t x + + 0 t 2 + + 2 2 Example: Motion with a constant acceleration Relations between x and v Given : vt () v a aavg t 0 a(t)constanta v(t0)v 0, x(t)x 0 Initial condition 0 v v at v v0 t 0 v v0 ( v0 at) 0 2 at x x + 0 t x + + ( v+ v0) ( v v0 0 t x + ) + + x x 0 + t 2 0 2 2 a 2 2 2 2 2 v vv0 + v0v v0 v v 0 2a 2a a 2 2 0 0 v v 2 a( x x )

Example: Motion with a constant acceleration Relations between v and t, x and t, x and v Given : a(t)constanta v(t0)v 0, x(t)x 0 Initial condition v and t : x and t : v v0 + a t 1 x x0 + v0t+ at 2 2 v and x : 2 2 0 0 v v 2 a( x x ) Free Fall Y Y 0 g Y0

+ Today, we learned

Motion along a straight line -the simplest type of motion Position: x(t) meters Velocity: v(t) meters/second Acceleration: a(t) meters/second 2 All are vectors: have direction and magnitude. Motion with a constant acceleration Relations between v and t, x and t, x and v Given : a(t)constanta v(t0)v 0, x(t)x 0 Initial condition v and t : x and t : v v0 + a t 1 x x0 + v0t+ at 2 2 Very very important!!! v and x : 2 2 0 0 v v 2 a( x x )

Homework : U Texas Homework service Ch.1, due Jan 26 Fri Ch2. Due Feb 2 Fri Quiz for ch.2: Feb 1 Reading assignment : Ch.2 (Sec. 1~7, Sec.9) Quiz #1 Chapter 1: Measurement SI unit, changing units, length, mass, time Honor Code violations NJIT has a zero-tolerance policy regarding cheating of any kind. Any incidents will be immediately reported to the Dean of Freshman Studies. In the cases the Honor Code violations are detected, the punishments range from a minimum of failure in the course plus disciplinary probation up to expulsion from NJIT with notations on students' permanent record. Avoid situations where honorable behavior could be misinterpreted.