Four Chapter 2

• Acceleration - Rate of change of velocity
  • Acceleration is a vector.

• The slope of the v-t graph is acceleration. (Sign is important)
• The v-t graph for uniform acceleration is a straight diagonal line.
• Uniform Acceleration - equal changes in speed in equal time intervals.
  • acceleration = a constant
• negative acceleration is left or down (Not slowing down)
• Some examples of uniform acceleration are:
  • a ball falling for a short distance
  • charged particles in an electric field
• An example of non uniform acceleration would be a chain falling off a table.

• Instantaneous acceleration is the rate of velocity change in an instant in time.
• If the acceleration is not uniform, then the v-t graph is a curved line.

• The slope of the tangent to a v-t graph is the instantaneous acceleration.
• The slope of a chord on a v-t graph is the average acceleration.
• If the acceleration is uniform:
  • a_inst = a_av
  • v-t graph is a straight line.
• If acceleration is not uniform:
  • a_inst not necessarily equal to a_av
  • v-t graph is a curved line.

• From a v-t graph, if you find the instantaneous acceleration (the slope of the tangent to the v-t graph) at various different times, a table of values can be established for plotting an acceleration-time (a-t) graph.
• An alternative method would be to use the method described previously in your notes:

• For the above v-t graph, the corresponding a-t graph is shown. Consider section A
  • Ask what kind of line do I have on the given graph? Þ Straight diagonal
  • Ask what kind of motion does this line represent? Þ Uniform acceleration
  • Ask what kind of line on the graph to be produced represents the type of motion? Þ Straight horizontal (the slope of v-t graph in section A is a constant +2.5 m/s²)
  • Sketch in the line. Þ Shown on a-t graph.
• You should go through each section of the v-t graph and see why the corresponding a-t graph is drawn as shown.
• To go to a v-t graph from an a-t graph, again, the area between the line and the time axis gives the velocity change in a time interval. Use this principle, and the above a-t graph, to see if you can construct the v-t graph given above.
• Note that the area above the time axis is a + change in velocity. Area below the time axis is a negative change in velocity.
• To know the final velocity (V_f), we must know the initial velocity (V_i).
• The following diagram summarizes how you can convert from one graph to another.

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October 29, 2013