# Vectors/ Calculus with i and j components

## Homework Statement I don't understand how to form an equation using the knowledge that, 'When ##t=4##, ##P## is moving parallel to the vector ##\mathbf {j}##'. I've seen the solution, and not a single part of it makes sense. I haven't attempted any question like this before, so I have no idea where to even start.

What I do know is how the whole integration/ differentiation process works to get between displacement, velocity and acceleration. That's only with normal equations though, not ##\mathbf {i}## and ##\mathbf {j}## components. So, I don't see any of what I do know already helping me here. Any help would be appreciated.

## The Attempt at a Solution

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haruspex
Homework Helper
Gold Member
how to form an equation using the knowledge that, 'When t=4, P is moving parallel to the vector ##\mathbf {j}##.
Can you write down the velocity vector? The i and j do not really create any complication for that. Just treat them as unknown constants.

Would I have to differentiate the position vector...?

haruspex
Homework Helper
Gold Member
Would I have to differentiate the position vector...?
Yes.

I got: $$v=(\frac 1 2t^3-4\lambda t) \mathbf i + (10t-\lambda) \mathbf j$$

Uh, I don't think that this question can be solved so I'm going to close it; I don't believe that I have the ability yet. Thanks for the help anyway

haruspex
I got: $$v=(\frac 1 2t^3-4\lambda t) \mathbf i + (10t-\lambda) \mathbf j$$