Velocity of the particle
Determine the Velocity of the particle in terms of component veocities?
Expert
Velocity is rate of change of DISPLACEMENT, and the particle is moving or DISPLACING in x and y directions, and through the image or snapshots the positions are recoded.
The displacement in x or y direction will be change in subsequent position values, such as x2 – x1 or y2 – y1, or Xi+1 – Xi. and is denoted by dX or ΔX.
Similarly the change is time, when the change in position occurs, is t2 – t1 or dtor Δt.
Now velocity is rate of change of displacement, i.e. dx/dt = ΔX/Δt = (Xi+1 – Xi)/(ti+1 – ti)
Delta t or ?t is the time duration between successive positions, which are recorded on successive images, now since there are 3000 frames per second. Hence 1/3000 seconds per frame.
This means that time duration or delta t between successive images and hence positions is 1/3000 sec.
Now velocity is (Xi+1 – Xi)/(ti+1 – ti) = (Xi+1 – Xi)/(1/3000)
But this is velocity in X direction only and since the particle is displaced in y direction as well you need to find velocity in Y direction also.
(Yi+1 – Yi)/(ti+1 – ti) = (Yi+1 – Yi)/(1/3000)
The velocity of the particle will be vector addition of these component velocities. In other words, you can calculate the velocity as, (VXi2 + VYi2)1/2.
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