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

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

  2. 2.A trolley is doing 5 m/s and accelerates steadily at 3 m/s² for 4 s. Use v = u + at. What is its final velocity, in m/s? Answer with a number.

  3. 3.Match each thing you can read off a motion graph to the quantity it gives.

    • The slope of a position-time line
    • The slope of a velocity-time line
    • The area under a velocity-time line
    • The displacement
    • The average velocity
    • The acceleration

  4. 4.A position-time graph comes out as a smooth curve rather than a straight line. What does that say about the motion?

    • a) The velocity is constant and the acceleration is zero
    • b) The object is at rest at a fixed position
    • c) The velocity is changing, so the object is accelerating
    • d) The object moved along a curved path over the ground

  5. 5.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 metres? Answer with a number.

  6. 6.On a position-time graph an object is at 30 m at 2 s and at 105 m at 5 s. What is the magnitude of its average velocity, in m/s? Answer with a number.

  7. 7.A car is doing 12 m/s when the driver brakes at a steady −3 m/s² until it stops. Use v² = u² + 2as. How far does it travel while braking, in metres? Answer with a number.

  8. 8.Two objects, A and B, are drawn on one position-time graph. B's line is steeper than A's. What follows?

    • a) B started further from the origin than A
    • b) The two have the same average velocity
    • c) B has the greater magnitude of average velocity
    • d) A has the greater magnitude of average velocity

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

  1. 1. 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
  2. 2. 17
  3. 3. The slope of a position-time line → The average velocity; The slope of a velocity-time line → The acceleration; The area under a velocity-time line → The displacement
  4. 4. c) The velocity is changing, so the object is accelerating
  5. 5. 25
  6. 6. 25
  7. 7. 24
  8. 8. c) B has the greater magnitude of average velocity