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Year 10 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.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.

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

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

  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 metres? Answer with a number.

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

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

  5. 5.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 average velocity
    • The displacement
    • The acceleration

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

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

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

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

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

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

Answer key — Year 10 Science — Motion graphs and the kinematic equations

  1. 1. 24
  2. 2. c) The velocity is changing, so the object is accelerating
  3. 3. 25
  4. 4. d) Zero, because the velocity is not changing
  5. 5. 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
  6. 6. b) When the acceleration stays constant through the motion
  7. 7. 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
  8. 8. d) The graph is not a route map — its rise shows position changing with time