How Does Particle P's Motion Change After 2 Seconds?

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The discussion centers on determining the motion of particle P after 2 seconds, given its initial position, velocity, and constant acceleration. The particle starts at (2,6) and moves with a velocity of (3i + j) ms-1 and acceleration of (16i + 24j) ms-2. Participants emphasize the need to show calculations to confirm that the particle moves directly away from the origin O and to find its speed at that time. There is confusion about the approach and formulas required to solve the problem, with a suggestion that moving directly away from O might imply a northward direction. Overall, the thread seeks guidance on the correct mathematical methods to analyze the particle's motion.
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Can anyone help me with this question, please?

A particle P is initially at the point (2,6) in relation to an origin, O, and is moving with velocity (3i + j) ms-. It has constant acceleration (16i + 24j) ms-. Show that after 2 seconds it is moving directly away from O, and find its speed at that time.

I would greatly appreciate any help, also details of how to get the answer would be excellent!

Thanks.
 
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Welcome to the forums. Please note that, for homework questions, you are required to show some work before we can help you. Also, in the future, please post in the relevant homework/coursework forum.

So, how do you think you'll approach this question?
 
Sorry about not posting this in the correct place.

Well with this question, I was not sure about what I need to work out. Considering it is asking for me to firstly show its moving directly away from O, I thought that this may mean that moving directly away is the same as traveling due North (where i = 0).

The initial point (2,6) in component form would be (2i + 6j) with a magnitude of 6.32.

Though I am unsure as to what formula I need to apply to calculate the answer. (sorry for sounding so uncertain!)
 

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