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Velocity of the particle

Determine the Velocity of the particle in terms of component veocities?

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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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