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.
(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
(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.