Unit 2: 1-D Constant Motion

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

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 = ∆d = df-di ∆t tf-ti

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 10.44 m/s?

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

When describing motion do 2 things: Describe what the Y is doing Describe what the slope is doing

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 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?

Positive slope/above line = + position Neg slope/below line = - position

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