Uniform Acceleration in One Dimension: Motion is along a straight line (horizontal, vertical or slanted).Motion is along a straight line (horizontal, vertical or slanted). Changes in motion result from uniform acceleration.Changes in motion result from uniform acceleration.

Distance and Displacement Distance is the length of the actual path taken by an object. Consider travel from point A to point B in diagram below: A B d = 20 m Distance is a scalar quantity (no direction): Contains magnitude only and consists of a number and a unit. (20 m, 40 mi/h, 10 gal)

Distance and Displacement Displacement is the straight-line separation of two points in a specified direction. Denoted by either D or x A vector quantity: Contains magnitude AND direction, a number, unit & angle. (12 m, 30 0 ; 8 km/h, N) A B D = 12 m, 20 o 

Distance and Displacement For motion along x or y axis, the displacement is determined by the x or y coordinate of its final position. Example: Consider a car that travels 8 m, E then 12 m, W.For motion along x or y axis, the displacement is determined by the x or y coordinate of its final position. Example: Consider a car that travels 8 m, E then 12 m, W. Net displacement D is from the origin to the final position: What is the distance traveled? 20 m !! 12 m,W D D = 4 m, W x 8 m,E x = +8x = -4

Definition of Speed Speed is the distance traveled per unit of time (a scalar quantity).Speed is the distance traveled per unit of time (a scalar quantity). s = = dtdt 20 m 4 s v = 5 m/s Not direction dependent! A B d = 20 m Time t = 4 s

Definition of Velocity Velocity is the displacement per unit of time. (A vector quantity.)Velocity is the displacement per unit of time. (A vector quantity.) v = 3 m/s at 20 0 N of E Direction required! A B d = 20 m Time t = 4 s D=12 m 20 o

Example 1. A runner runs 200 m, east, then changes direction and runs 300 m, west. If the entire trip takes 60 s, what is the average speed and what is the average velocity? Recall that average speed is a function only of total distance and total time: Total distance: s = 200 m m = 500 m Avg. speed 8.33 m/s Direction does not matter! start s 1 = 200 m s 2 = 300 m

Example 1 (Cont.) Now we find the average velocity, which is the net displacement divided by time. In this case, the direction matters. x o = 0 t = 60 s x 1 = +200 m x f = -100 m x 0 = 0 m; x f = -100 m Direction of final displacement is to the left as shown. Average velocity: Note: Average velocity is directed to the west.

Average and Instantaneous v xx tttt x2x2x2x2 x1x1x1x1 t2t2t2t2 t1t1t1t1 xx tt Time slope Displacement, x Average Velocity: Instantaneous Velocity:

Definition of Acceleration  An acceleration is the change in velocity per unit of time. (A vector quantity.)  Units are in m/s 2.

Example of Acceleration The wind changes the speed of a boat from 2 m/s to 8 m/s in 3 s. Each second the speed changes by 2 m/s. Wind force is constant, thus acceleration is constant. + v f = +8 m/s v 0 = +2 m/s t = 3 s Wind

Motion Graphs Let’s go over the basics.

Displacement vs. time graphs (x vs. t) Shows the change in position for an object over a period of time. The slope of the line at any point shows the velocity of the object. What is the velocity of this object from t=1 to t=3 seconds? –20 m/s

displacement vs. time graphs (x vs. t) A parabolic curve means that the slope (velocity) is not constant, so the object is accelerating.

Velocity vs. time graphs (v vs. t) Shows the change in velocity for an object over a period of time. The slope of the line at any point shows the acceleration of the object. What is the acceleration of this object from t=4 to t=8 seconds? 5 m/s 2

Velocity vs. time graphs (v vs. t) The total area under the line tells you the displacement (change in position) for the object in motion. What is the displacement of the object from t=0s to t=8s? 160 m

Acceleration vs. time graphs (a vs. t) These graphs are boring, and will only have a straight line above the axis, below the axis, or at 0. But what does the straight line mean? –Acceleration is always constant. What is the acceleration in this graph? –-2m/s 2 What does that mean? –Object is accelerating to the left.

Acceleration vs. time graphs (a vs. t) The total area under the line tells you the velocity for the object in motion. What is the change in velocity after the first 5 sec? -10 m/s