TIME CURVES AND TIME GRAPH Prepared by: Lordel Segovia
Position vs Time Curve Suppose Silver “the Helping Dog” runs away and suddenly stopped when she’s 5 m away from her home. Shen then decides to take a short 5 second rest in the grass. After her 5 second rest, she hears the dinner bell ring and returned back to her home. The position-time graph and table for her motion would look something like this:
Time (s) Position 0.0 0.0 1.0 1.0 2.0 2.0 3.0 3.0 4.0 4.0 5.0 5.0 6.0 5.0 7.0 5.0 8.0 5.0 9.0 5.0 10.0 5.0 11.0 3.0 12.0 1.0 13.0 0.0 Position-Time Table of the Dog
Position-Time Table of the Dog
Graph Visual representation of relationships between quantities such as position and time. The position-time graph and table of the motion of the dog is given.
First Part (Left Segment) This is the slope of the left segment. Slope, The dog travelled 5.0 m away from her home in 5.0 s. The numerator or “rise” is 5.0 m while the denominator or “run” is 5.0 s. Dividing rise over run gives the slope which is +1 m/s. The slope is expressed in m/s, the unit for velocity.
In a position-time graph the slope of any non vertical line gives the velocity . The rise of the slope gives the displacement while the run of the slope gives the change in time .
If the line is horizontal, its slope is zero. If the line is vertical, its slope is undefined. Second part (Middle Segment) Slop, m
Since the slope is zero, this means the velocity is 0.0 m/s; the dog is not moving during this time interval. What do you think the dog is probably doing?
A horizontal line on a position time-graph indicates zero velocity or a body is at rest.
Third part (Right Segment) Slope, m The slope is negative because the rise of the slope or displacement is negative. The quotient of the rise by the run gives a velocity of -1.7 m/s. This means the dog traveled in the opposite direction.
A line with a negative slope in a position-time graph indicates movement with constant speed in the opposite direction. Take the absolute values of the slopes of the two lines; (1.0m/s) for the line on the left and (1.7 m/s) for the line on the right. By visual inspection and comparison of the two lines, the line on the right has a steeper orientation. Therefore, the dog was moving faster here during the last seconds than she was during the first seconds, regardless of direction.
Graphically, a slant line ( to the left or right) indicates the direction. A steeper slope, however, means, a greater rise compared to the run. It indicates a greater speed component for the velocity as the moving object covers more distance per unit time.
A position-time graph with a steep slope means the moving object covers more distance per unit time, indicating a faster speed.
Practice A. Construct the Velocity vs Time and Position vs Time Graphs of the Following Tables B. Interpret your graph by determining the slope of each line. Velocity (m/s) Time (s) 0.0 0.0 7.0 1.0 21.0 3.0 25.0 5.0 33.0 8.0 33.0 15.0 33.0 22.0
Position (m) Time (s) 0.0 0.0 10.0 3.0 29.0 5.0 38.0 8.0 40.0 11.0 40.0 15.0 40.0 17.0 45.0 19.0 50.0 23.0
1 Whole Answer immediately 1. What is a projectile motion? 2. What is the significance of studying the concept of projectile motion? 3. Give at least 10 fields where projectile motion is applied then draw these applications. (ex. Modern artillery)
Reference Ser John YT
1 Whole 1. What is your group’s film all about? 2. What is the significance of the science concept/invention presented in your film? 3. Imagine, write and draw a science concept/invention that you are interested in discovering/creating that the modern science have not tackled yet.