One-Dimensional Constant Motion Physics 1

Displacement The change in position of an object is called displacement,  x. Example 1: I go running on the 3-mile jogging loop at Memorial park in Houston. I do three (3) laps. I am really tired. What is my total displacement?

Definition displacement and distance TermDefinition Reference PointThe ‘zero’ point from which something is measured PositionDistance and direction (sign) from reference point DisplacementChange in position including direction (sign) between two position points. Two points are generally specified by associated times. Standard SI units are meters (m) (pick me up from my bike ride, where did I park?) DistanceActual distance travelled. Magnitude of displacement. (how far I rode or ran, how tired am I?)

A Position Time graph shows position plotted against time.

To Find Position at a given time (e.g. 50 s)

To Find time at a given position (e.g. 3 m)

OR

To Find DISPLACEMENT between two points (e.g. 20s and 60s) 1. Find position at final time -- 4 m) 2.Find position at start time -- 2 m) 3.Calculate change in position. Final – Start (4 m ― 2 m = 2 m) 1. Find position at final time -- 4 m) 2.Find position at start time -- 2 m) 3.Calculate change in position. Final – Start (4 m ― 2 m = 2 m)

To Find DISTANCE between two points (e.g. 0s and 100s) 1.Find all displacements in each direction (e.g. : 0-40: 4-0=4m 40-60: 4-4=0m 60-80: 0-4=-4m : 0-0=0m ) 2.Add “absolute value” or magnitudes of all displacements (4+0+|-4|+0 = 8m) 1.Find all displacements in each direction (e.g. : 0-40: 4-0=4m 40-60: 4-4=0m 60-80: 0-4=-4m : 0-0=0m ) 2.Add “absolute value” or magnitudes of all displacements (4+0+|-4|+0 = 8m)

Speed or Velocity? Speed and velocity are different quantities. Speed is the rate distance covered of over time. Speed is a scalar quantity. Velocity is the rate displacement traveled over time. Velocity is a vector quantity. Speed and velocity differ when an object changes direction in its motion.

Definition velocity and speed TermDefinition Velocity (average velocity) Displacement divided by time. Change in position divided by time. Change per time (e.g. mph or Miles per hour) Standard SI units are meters per second (m/s) Slope of a position-time graph. Includes a direction / sign. + positive if increasing distance from reference point. getting further away, ― negative if decreasing approaching reference point. SpeedPositive ‘magnitude’ of velocity (no direction specified)

Position vs. Time Graph A position vs. time (d-t) graph plot of position as a function of time. The d-t graph of a uniformly moving object is linear in shape.

Position vs. Time Graph The slope of a linear graph is the rise (  y) over the run (  x). The slope of an d-t graph describes the average velocity of object in motion. For a d-t graph…

To Find average VELOCITY between two points (e.g. 20s and 40s) 1. Find displacement (2m from previous exercise) 2.Find change in time (40s-20s=20s) 3.Divide change in distance by change in time 2m/20s = 0.1 m/s 1. Find displacement (2m from previous exercise) 2.Find change in time (40s-20s=20s) 3.Divide change in distance by change in time 2m/20s = 0.1 m/s

To Find average VELOCITY between two points (e.g. 20s and 60s) 1. Find displacement (2m from previous exercise) 2.Find change in time (60s-20s=40s) 3.Divide change in distance by change in time 2m/40s = 0.05 m/s 1. Find displacement (2m from previous exercise) 2.Find change in time (60s-20s=40s) 3.Divide change in distance by change in time 2m/40s = 0.05 m/s

Different Types of Speed Instantaneous Speed - the speed of an object at a given instant. Average Speed – the speed of an object as it covers the total distance traveled over the total time interval.

Example 2 A brand new car has an odometer reading of 50 km after 45 minutes of travel. What is the average speed of the car in km/hr? __ ∆ V = ∆x = x f -x i ∆t t f -t i

Example 3 According to Google Maps it will take 4.5 hours via I-45 if you travel by car from Sugarland to Dallas which is 418 km in total distance. Calculate the average speed in km/hr.

Example 4 What was the record time of Usain Bolt during the 100-m event in 2009 if he ran m/s?

Definition acceleration TermDefinition Acceleration (average acceleration) Change in velocity over time. Standard SI units are meters per second ( ) Slope of a velocity-time graph. Includes a direction / sign. + positive if increasing (going faster in positive direction or getting slower in negative direction). getting further away, ― negative if decreasing (going slower in positive direction or going faster in a negative direction) Will show as a curved line on a position time graph

Velocity vs. Time Graph A velocity-time (v-t) graph plot of velocity as a function of time. The v-t graph of a uniformly moving object is a horizontal line. Velocity is constant!

Velocity vs. Time Graph The v-t graph of an object moving at a non-uniform rate is a sloped line. The velocity is changing at a constant rate.

Velocity vs. Time Graph The slope of a v-t graph describes the rate of change in velocity over time.

Constant Velocity

Example 6 Describe the motion at each letter

Velocity vs. Time Graph In the given v-t graph, the area under the graph is a rectangle. area = l x w = v x  t v x  t =  x (displacement) The area under a v-t graph is equal to the displacement traveled over time.

Velocity vs. Time Graph In the given v-t graph, the area under the graph is a triangle. area = ½ x b x h = ½ x  t x v =  d (displacement) The area under the v-t graph is still equal to the displacement traveled over time.

Example 7 What is the displacement of the object from sec?

Example 8 What is the displacement of the object from 0-4 sec?