Velocity of moving object at x and y axis
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I want to calculate the velocity and acceleration of a moving object. I have the centroid value and i am calculating the distance covered by using euclidean distance formula on current and previous centroid. I am confused on how do we calculate velocity and acceleration of a moving object at x and y-axis. Do we simply divide the euclidean distance formula into x(centroid x) and y(centroid y) parts?
2 Comments
KSSV
on 6 Apr 2017
Velocity is defined as displacement over time. You have distance now, do you have time?
Accepted Answer
Jan
on 6 Apr 2017
Edited: Jan
on 6 Apr 2017
You can get the velocities in X and Y direction independently.
Vx = gradient(X, TimeStep);
Vy = gradient(Y, TimeStep);
Or:
S = blobCentroid - PrevCent;
V = gradient(S, TimeStep);
Now V contains teh X and Y component.
3 Comments
Jan
on 6 Apr 2017
@BlueBee77: Start with defining, what you want to know: If you want the velocities in X and Y direction separately, you do not need the Euclidean distance. If you want the total velocity independent from the direction, the Euclidean distance will solve this. Or you can calculate the velocities in X and Y direction at first, and then V_total = sqrt(V_x ^ 2 + V_y ^ 2).
It might get clear with an example: The object travels from the point (1, 2) to (2, 4) in 1 time unit h (e.g. seconds, but we can omit the units here). Then:
V_x = (2 - 1) / h = 1
V_y = (4 - 2) / h = 2
V_total = sqrt(1^2 + 2^2) = 2.236
Or you use the Euclidean distance:
V_total = Dist / h = sqrt((2 - 1)^2 + (4 - 2)^2) / h = 2.236
Both calculations are equivalent. In fact, the same numbers appear in the same equations.
More Answers (1)
Image Analyst
on 6 Apr 2017
You can use diff(distances) to get "instantaneous" velocity. Then again on velocity to get acceleration. Or use diff(x) and diff(y) to get velocity components along the two directions separately.
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