How to read a position vs. time graph. Interpreting Motion How to read a position vs. time graph.

Position vs. Time Graphs Stationary Constant positive velocity Constant negative velocity

Position vs.Time graphs Changing velocity (increasing) Changing velocity (decreasing)

If you want to know what the average velocity is calculate the slope. Slope = Δd / Δt =Vavg Δd = df - di Δt = tf - ti

Using slope to predict motion On a position vs. time graph If slope is 0, then velocity is 0. If slope is positive, velocity is constant in positive direction. If slope is negative, velocity is constant in the opposite direction. If slope is changing, velocity is changing. (i.e. you are accelerating)

Object A is stationary at some positive position from the origin. d(m) A Object A is stationary at some positive position from the origin. t(s)

Object B moves away from origin with a constant positive velocity. d(m) B Object B moves away from origin with a constant positive velocity. t(s)

d(m) C Object C starts at a positive position and moves away from the origin with a constant positive velocity. t(s)

Object D moves away from the origin at a constant positive velocity. t(s)

d(m) C Same velocity as B. B A D Slower than B or C. t(s)

On a separate sheet of paper. 1.You are to describe the motion of each walker (A-E) in the next slide. Your description should include… Where the walker started Which direction the walker moved Where the walker stopped A description of the motion (constant, speed up, slowing down, or stationary). A comparison of relative speed. Who is fastest ? slowest?

E A East #1 B High St. D C West

2. Describe the motion of the car shown in the next slide. 3. Answer the following questions using the next slide. When was the car 20m west of the origin? Where was the car at 60s? When and where did the car suddenly reversed direction?

East

Finding the Equation (Click to view notes.) m = ∆y/∆x (6m- 4m)/ (2s-1s)= 2m/s d = 2t+2 y = y = mx +b b x =

Finding position (Click to view equations.) Vavg = Δd / Δt Vavg = (df –di)/Δt df = di + Vavg Δt y = b + mx

#4-5 B C

Use the next slide to answer the following questions. 4. Consider the motion of rider A Write the equation that represents the motion. Where will the rider be at 1.0s? 5. Consider the motion of rider C Write the equation that represent the motion. When will rider C be at -10.0m?

6. Draw a position-time graph for a person who starts at a positive position walks with uniform motion toward the origin. 7. Repeat (on same graph) for a person that starts at a negative position and walks toward the origin with uniform motion. 8.Draw a new position-time graph for a person who walks one meter at a moderate speed, waits for a short time, walks the next meter slowly, and then walks the final meter quickly.

All answers should be turned in before you leave class All answers should be turned in before you leave class. Please put your name and period number on your paper. (Yes this is worth points!)

Answers #1 A starts at high street, walks at a constant speed toward the east. B starts W of high street and walks east at constant rate but slower than A. C starting at high street walking west very fast at first then slowing to a stop. D starting east of high street walking very quickly (faster than A or B) toward the west. E starts at high street walking east slowly at first then increasing speed toward .

Answers #2-5 2. Object goes from 0 to -20 m in 10 s at a constant velocity then stays stationary at -20m for 30 s, then goes from -20 m to 30 m in 20 s at a constant velocity, then goes from 30m to 0m in 20 seconds at a constant velocity. 3. a) 10-30 s b) 15 m c) 30 m, 50 s 4. d= +10t - 2 5. d= -6.7t - 2

Answers #6-8 #6 red line #7 green line #8 Please note the difference in slope. More slope=greater velocity.