An ant starts from the origin and walks along a straight line. After every second, its position (in mm) is observed by a curious 5-year old. These are his readings:
Position (mm) 0 10 40 100 200
After time (s) 0 1 2 3 4
By looking at this table, which of the following could be a possible description of the ant's motion is
(a) Uniform velocity (b) uniform acceleration (with non-uniform velocity
(c) Uniform jerk (with non-uniform accelerator) (d) cannot be determined (can be any of the above)
An ant starts from the origin and walks along a straight line. After every second, its position (in mm) is observed by a curious 5-year old. These are his readings:
Position (mm) 0 10 40 100 200
After time (s) 0 1 2 3 4
By looking at this table, which of the following could be a possible description of the ant's motion is
(a) Uniform velocity (b) uniform acceleration (with non-uniform velocity
(c) Uniform jerk (with non-uniform accelerator) (d) cannot be determined (can be any of the above)
The correct option is C Uniform jerk (with non-uniform accelerator)
The ant's positions at the times don't seem to form any obvious pattern.
x 0 10 40 100 200
One of the things we can try is see if the differences from a pattern. That will give a picture about velocities, won't they? (You know that avg. velocity is just the change/unit time of position of the ant) writing down first order differences
0 10 40 100 200
10 30 60 100
Ok, nothing as of yet. Let's try second order differences; let's try to get some pattern in the acceleration.
10 30 60 100
20 30 40
Great! So now I can see that the acceleration is also increasing but it is an arithmetic progression. So finally calculating third order differences, we get
20 30 40
10 10 → constant
Thus, the rate of change of acceleration (what's called the jerk) could be a constant. But clearly, the velocity and the acceleration are variable. So, only possibility is constant jerk. Hence, Option (c).
Uniform jerk (with non-uniform accelerator)
The ant's positions at the times don't seem to form any obvious pattern.
x 0 10 40 100 200
One of the things we can try is see if the differences from a pattern. That will give a picture about velocities, won't they? (You know that avg. velocity is just the change/unit time of position of the ant) writing down first order differences
0 10 40 100 200
10 30 60 100
Ok, nothing as of yet. Let's try second order differences; let's try to get some pattern in the acceleration.
10 30 60 100
20 30 40
Great! So now I can see that the acceleration is also increasing but it is an arithmetic progression. So finally calculating third order differences, we get
20 30 40
10 10 → constant
Thus, the rate of change of acceleration (what's called the jerk) could be a constant. But clearly, the velocity and the acceleration are variable. So, only possibility is constant jerk. Hence, Option (c).
