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Grade 9 Science — Motion graphs and the kinematic equations

Read velocity off the slope of a position-time graph and displacement off the area under a velocity-time graph, and use v = u + at, s = ut + ½at² and v² = u² + 2as.

Name: ________________________

Before you start

The parts of a position-time graph, each one named.

123
  1. 1. The time axis, along the bottom
  2. 2. The position axis, up the side
  3. 3. The position-time line itself

This line is straight and sloping, so the object is covering equal ground in equal times. How steeply it climbs is how fast it is going.

  1. 1.Three position-time graphs are sketched below. Tap the one that shows an object at rest.

    Write the number of the part.

    123

  2. 2.Put the steps for plotting a motion graph in order, starting by drawing two perpendicular axes and marking where they cross as the origin.

    • Choose a scale for each axis
    • Join the plotted points to make the graph
    • Mark the values along each axis
    • Decide which quantity goes along each axis
    • Draw two perpendicular axes and mark where they cross as the origin
    • Plot a point for each pair of readings

  3. 3.A cart starts from rest and accelerates steadily at 2 m/s² for 5 s. Use s = ut + ½at². How far does it travel, in meters? Answer with a number.

  4. 4.A child looks at a position-time graph whose line climbs steadily and says the object must have traveled uphill. What has she misread?

    • a) The graph is not a route map — its rise shows position changing with time
    • b) Nothing; a rising line does mean the object went uphill
    • c) A rising line means the object was slowing down
    • d) The graph shows velocity up the side, not position

  5. 5.When may the three kinematic equations be used?

    • a) When the velocity stays constant through the motion
    • b) When the object is at rest
    • c) For any motion whatsoever
    • d) When the acceleration stays constant through the motion

  6. 6.Sort each graph shape by what it says about the object's velocity.

    Groups: Velocity stays constant · Velocity is changing

    • A straight sloping velocity-time line
    • A velocity-time line parallel to the time axis
    • A curved position-time line
    • A straight sloping position-time line

  7. 7.On a velocity-time graph, the line runs flat and parallel to the time axis. What is the acceleration?

    • a) Constant and opposite to the direction of motion
    • b) Constant and along the direction of motion
    • c) Zero, because the velocity is not changing
    • d) Rising steadily with time

  8. 8.A van holds a steady 12 m/s for 5 s. Read the displacement off the area under its velocity-time line. How far does it go, in meters? Answer with a number.

Answer key — Grade 9 Science — Motion graphs and the kinematic equations

  1. 1. 1 — The first graph, a flat line
  2. 2. 1. Draw two perpendicular axes and mark where they cross as the origin 2. Decide which quantity goes along each axis 3. Choose a scale for each axis 4. Mark the values along each axis 5. Plot a point for each pair of readings 6. Join the plotted points to make the graph
  3. 3. 25
  4. 4. a) The graph is not a route map — its rise shows position changing with time
  5. 5. d) When the acceleration stays constant through the motion
  6. 6. A straight sloping position-time line → Velocity stays constant; A velocity-time line parallel to the time axis → Velocity stays constant; A curved position-time line → Velocity is changing; A straight sloping velocity-time line → Velocity is changing
  7. 7. c) Zero, because the velocity is not changing
  8. 8. 60