Question

The graph below shows velocity as a function of time for some unknown object.

(i) what can we say about the motion of this object?

(ii) Plot the corresponding graphs of displacement and acceleration as functions of time.

Answer 1

(i)

1. The problem presents us with a velocity-time graph.
2. Do not read it as if it was showing you position.
3. You can't immediately determine where the object is from this graph.
4. You can say what direction it's moving, how fast it's going, and whether or not it's accelerating, however the motion of this object is described for several segments in the graph below.

(ii)

Plotting the corresponding graph of acceleration as a function of time:-

1. Acceleration is the rate of change of displacement with time.
2. To find acceleration, we need to calculate the slope in each interval.

1. Now, we can plot these values as a function of time. Since the acceleration is constant within each interval, the new graph should be made entirely of linked horizontal segments.

Plotting the corresponding graph of displacement as a function of time:-

1. Displacement is the product of velocity and time. To find displacement, we need to calculate the area under each interval.

1. Find the cumulative areas starting from the origin (given an initial displacement of zero)
2. 0 s → 0 = 0 m
   4 s → 0 + 8 = +8 m
   8 s → 0 + 8 − 8 = 0 m
   12 s → 0 + 8 − 8 − 16 = −16 m
   16 s → 0 + 8 − 8 − 16 − 8 = −24 m
   20 s → 0 + 8 − 8 − 16 − 8 + 0 = −24 m
   24 s → 0 + 8 − 8 − 16 − 8 + 0 + 8 = −16 m
   30 s → 0 + 8 − 8 − 16 − 8 + 0 + 8 + 24 = +8 m
3. Now we need to plot these values as a function of time.
4. Pay attention to the shape of each segment.
5. When the object is accelerating, the line should be curved.