Velocity of the particle

Question

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

Answer 1

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 X_i+1 – X_i. 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 = (X_i+1 – X_i)/(t_i+1 – t_i)

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 (X_i+1 – X_i)/(t_i+1 – t_i) = (X_i+1 – X_i)/(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.

(Y_i+1 – Y_i)/(t_i+1 – t_i) = (Y_i+1 – Y_i)/(1/3000)

The velocity of the particle will be vector addition of these component velocities. In other words, you can calculate the velocity as, (V_Xi² + V_Yi²)^1/2.