GRAPHS REVIEW

Consider the distance vs. time graph below for cyclists A and B: Warm-up: Consider the distance vs. time graph below for cyclists A and B: A B Distance (cm) Time (s) 5 Do the cyclists start at the same position? How do you know? At t = 7 s, which cyclist is ahead? Why?

Quick Notes Displacement: a change in position, or a change in distance from the starting location. Just like with velocity, direction matters when discussing displacement.

Quick Notes Example: I walked 1 km to the store and then walked 1 km back home. My distance traveled was 2 km. My displacement was 0 km (because I ended up back where I started).

Speed and Distance (con’t) Other equations for the speed and distance relationship (s = d / t): Distance = speed x time d = v t Time = distance /speed t = v / s Distance Time Slope = speed

Position vs Time Graphs Graphical record of motion can be used to determine: “where” and “when” for an object – read position for a given time or read the time for a certain position average velocity of the object

Equation of motion from graph y = mx + b y: final position d1 m: average velocity v x: time t b: initial position d0 Create equation of motion from graph d1= 5t +20 When will rider be at position = -20 m?

Interpreting motion from graph Estimate the time when runner was at the 65 meter position. Draw interpolation lines – start at 65 meters  graph line  draw line down to 6.5 seconds

Slope of Position – Time Graph displacement = rise slope of position vs time graph = average velocity vavg = 4 m/s slope calculations must take actual value not boxes  boxes

Velocity vs. Time

Graphing Notes: Summary Question: What does the area under the Velocity vs. Time graph tell you? 4 3 2 1 Velocity (m/s) Time (s) 1 2 3 4 5 Answer: It tells you the distance traveled (or displacement) of the object!

Graphing Notes: Summary It works for acceleration, too! 4 3 2 1 Velocity (m/s) Time (s) 1 2 3 4 5 What is the total displacement? (1/2bh=2(4)= 8 meters!

The 9-Graph Summary: (complete these graphs now) Constant Position (No Motion): Velocity Accel. Displacement Time T T V A D Constant Velocity: T T T V A Constant Acceleration: D T T T

The 9-Graph Summary: Constant Position (No Motion): Constant Velocity: Accel. Distance Time T T V A D Constant Velocity: T T T V A Constant Acceleration: D T T T

The 9-Graph Summary: Constant Position (No Motion): Constant Velocity: Accel. Distance Time T T V A D Constant Velocity: T T T V A Constant Acceleration: D T T T

The 9-Graph Summary: Constant Position (No Motion): Constant Velocity: Accel. Distance Time T T V A D Constant Velocity: T T T V A Constant Acceleration: D T T T

Which position-versus-time graph represents the motion shown in the motion diagram? STT2.1 (1) (2) (3) (4) (5)

Which position-versus-time graph represents the motion shown in the motion diagram? STT2.1 (1) (2) (3) (4) (5)

Which velocity-versus-time graph goes with this position-versus-time graph on the left? (1) (2) (3) (4) STT2.2

Which velocity-versus-time graph goes with this position-versus-time graph on the left? (1) (2) (3) (4) STT2.2

Which position-versus-time graph goes with this velocity- versus-time graph on the left? The particle’s position at ti = 0 s is xi = –10 m . STT2.3 (1) (2) (3) (4)

Which position-versus-time graph goes with this velocity- versus-time graph on the left? The particle’s position at ti = 0 s is xi = –10 m . STT2.3 (1) (2) (3) (4)

Which velocity-versus-time graph or graphs goes with this acceleration-versus-time graph? The particle is initially moving to the right and eventually to the left. STT2.4 (1) (2) (3) (4)

Which velocity-versus-time graph or graphs goes with this acceleration-versus-time graph? The particle is initially moving to the right and eventually to the left. STT2.4 (1) (2) (3) (4)

The slope at a point on a position-versus-time graph of an object is 1) the object’s speed at that point. 2) the object’s average velocity at that point. 3) the object’s instantaneous velocity at that point. 4) the object’s acceleration at that point. 5) the distance traveled by the object to that point. IG2.1

The slope at a point on a position-versus-time graph of an object is 1) the object’s speed at that point. 2) the object’s average velocity at that point. 3) the object’s instantaneous velocity at that point. 4) the object’s acceleration at that point. 5) the distance traveled by the object to that point. IG2.1

The area under a velocity-versus-time graph of an object is 1) the object’s speed at that point. 2) the object’s acceleration at that point. 3) the distance traveled by the object. 4) the displacement of the object. 5) This topic was not covered in this chapter. IG2.2

The area under a velocity-versus-time graph of an object is 1) the object’s speed at that point. 2) the object’s acceleration at that point. 3) the distance traveled by the object. 4) the displacement of the object. 5) This topic was not covered in this chapter. IG2.2

1) the 1-pound ball wins the race. A 1-pound round ball and a 100-pound round ball are placed side-by-side at the top of a frictionless hill. Each is given a very light tap to begin their race to the bottom of the hill. In the absence of air resistance 1) the 1-pound ball wins the race. 2) the 100-pound ball wins the race. 3) the two balls end in a tie. 4) there’s not enough information to determine which ball wins the race. IG2.4

1) the 1-pound ball wins the race. A 1-pound round ball and a 100-pound round ball are placed side-by-side at the top of a frictionless hill. Each is given a very light tap to begin their race to the bottom of the hill. In the absence of air resistance 1) the 1-pound ball wins the race. 2) the 100-pound ball wins the race. 3) the two balls end in a tie. 4) there’s not enough information to determine which ball wins the race. IG2.4