Do now In your Physics notebook please start a page titled: One-Dimensional Constant Motion Below it, please define the following terms in your own words: Distance Displacement

One-Dimensional Constant Motion Physics 1

Key terms Distance Displacement Time Speed Velocity Scalar Vector Instantaneous Average Velocity Scalar Vector

Displacement The change in position of an object is called displacement, Dx. 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?

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

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 __ ∆ V = ∆x = xf-xi ∆t tf-ti 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?

Example 3 __ ∆ V = ∆x = xf-xi ∆t tf-ti 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 10.44 m/s?

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 (constant speed) object is linear in shape.

A Position Time graph shows position plotted against time.

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

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

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

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

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

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

Example 5 Bob is driving west at a constant 60 mph. Plot time vs. distance and graph What if Bob started 75 miles from home? What if Bob was going 30 mph? What is the relationship between distance/velocity/time?

Describe the motion at each point

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.

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

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 Dt v x Dt = Dx (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 Dt x v = Dd (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 10-16 sec?

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

POS vs Time or VEL vs Time?