Working with Graphs cont’d

Steps for finding slopes and what the slope means:

  • Pick two points on the line and determine their coordinates.
  • Determine the difference in y-coordinates of these two points (rise).
  • Determine the difference in x-coordinates for these two points (run).
  • Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).
  1. Consider the graph. Note that the slope is not positive but rather negative; that is, the line slopes in the downward direction. Note also that the line on the graph does not pass through the origin. Slope calculations are relatively easy when the line passes through the origin since one of the points is (0,0). But that is not the case here. Test your understanding of slope calculations by determining the slope of the line.

Slope = ______

  1. Determine the velocity (i.e., slope) of the object as portrayed by the graph below.

Slope = ______

  1. Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that are true): Selections are: ______
  1. moving in the positive direction.
  2. moving with a constant velocity.
  3. moving with a negative velocity.
  4. slowing down.
  5. changing directions.
  6. speeding up.
  7. moving with a positive acceleration.
  8. moving with a constant acceleration.
  1. The velocity-time graph for a two-stage rocket is shown below. Use the graph and your understanding of slope calculations to determine the acceleration of the rocket during the listed time intervals.

A)t = 0 - 1 second = ______

B)t = 1 - 4 second = ______

C)t = 4 - 12 second = ______

  1. Describe the motion depicted by the following velocity-time graphs. In your descriptions, make reference to the

A) direction of motion (+ or - direction),

B) the velocity and acceleration and

C) any changes in speed (speeding up or slowing down) during the various time intervals (e.g., intervals A, B, & C).

A) ______

B) ______

C) ______

A) ______

B) ______

C) ______

A) ______

B) ______

C) ______

  1. Use your Formula Chart to calculate the following, the equation you end up using will have to be manipulated. Show equation, Show manipulation work, Show plugging in #’s, Box in answer.

You let your bike roll down a ramp beginning from rest and it accelerates uniformly. The bike rolls 125 m in 25 s, what is your rate of acceleration on the bike?

(Use graph below to answer questions 7 – 13)

  1. ______Which object(s) is/are maintaining a state of motion (i.e., maintaining a constant velocity)?
  1. ______Which object(s) is/are accelerating?
  1. ______Which object(s) is/are not moving?
  1. ______Which object(s) change(s) its direction?
  1. ______On average, which object is traveling fastest?
  1. ______On average, which moving object is traveling slowest?
  1. ______Which object has the greatest acceleration?

(Use graph below to answer questions 7 – 13)

  1. ______Which object(s) is/are maintaining its state of motion?
  1. ______Which object(s) is/are accelerating?
  1. ______Which object(s) is/are not moving?
  1. ______Which object(s) change(s) its direction?
  1. ______Which accelerating object has the smallest acceleration?
  1. ______Which object has the greatest velocity?
  1. Sketch a position-time graph for an object which is moving with a constant, positive velocity.