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I’m familiar with scale diagrams where three forces act upon an object and trigonometry is used to find the resultant force, but I’ve come across questions that use units of velocity instead of force.

What does it mean when a diagram says an object has multiple velocities?

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  • $\begingroup$ I've not seen these called scale diagrams. This looks like a pictorial representation of vector addition, or the decomposition of a vector into components. It does not have to be a force. The same applies to any vector. Is this an example of relative motion? Like a canoe on moving water and you are looking for the velocity relative to the land? $\endgroup$ – ggcg May 10 at 16:30
  • $\begingroup$ The interpretation will always partly depend on the context. Can you share the full problem? The diagram seems to refer to a particle whose initial velocity was $20 \textrm{ m/s}\hat{i}$, and whose final velocity was $20 \textrm{ m/s}\hat{j}$. So the diagram is telling you that the particle experienced a change in velocity ($\Delta \vec{v}$). $\endgroup$ – Rodney Dunning May 10 at 16:31
  • $\begingroup$ Yes, ggcg you are right it was a canoe on moving water, but the question gave me two sides of a right angled triangle, I just used Pythagoras to find the other side , but i found the question Baffling on a conceptual level $\endgroup$ – Ubaid Hassan May 10 at 16:51
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Both force and velocity are vector quantities.

This means that they can be split up into components.

Here you have been given two components of a velocity and need to use trigonometry to calculate the "resultant velocity". I.e. reconstruct the velocity components back to the "total", true velocity.

This is analogous to saying that I am walking East at $20ms^{-1}$ on a boat which is moving North at $20ms^{-1}$ and then asking: what is your velocity relative to the sea. Clearly we need to add the two vector quantities.

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