Kinematics Graph

Three types

  • Distance-time graph (d-t)
  • Speed-time graph (v-t)
  • Acceleration-time graph (a-t)

Relationships

Detailed Illustration

Example:

A girl starts from rest and travels along a straight line. The diagram below shows the velocity-time graph of the girl from 0 s to 90 s.
(a)  Describe the motion of the girl from 0 s to 40 s.
(b)  Find the average velocity of the girl in the first 70 s.
(c)  Draw the acceleration-time graph of the girl from 0 s to 90 s.
(d)  Find the displacement of the girl from the starting point to the position at 90 s.
Answer:
(a) From 0 s to 20 s, she travels with constant acceleration of 0.25 ms^(-2);
      From 20 s to 40 s, she travels at constant velocity of 5 m/s.
(b) Total displacement = area under v-t graph
                                        = ½ (30 + 70) * 5 = 250 m
      Average velocity = 250/70 = 3.57 m/s
(c) Acceleration is the gradient of v-t graph.
(d) Displacement = area under v-t graph
                              = 250 – ½ * 20 * 5 = 200 m

Tips:
(1) It is very easy to mix up kinematics graphs. The only way to differentiate these graphs is to look at the y-axis!
(2) When describing the motion, do it region by region! And always talk about acceleration or speed / velocity with values if applicable. Refer to example above. 
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