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1. Hey all, I'm stuck on the following question:

"A particle has an initial velocity of i + 2j and is accelerating in the direction i + j. If the magnitude of the acceleration is 5 root 2, find the velocity vector and the speed of the particle after 2 seconds."

2. i think this means it has an acceleration of 5root 2 in direction of the hypotenuse of a triangle with 1 1 root2 as sides therefore 2x^2 =50 therefore its acceleration with magnitude 5 in each direction therefore after 2 seconds it will have increased by 10 m/s add that onto original values. i dont know if this is the case we didnt have vectors in our mechanics because ocr is crap
3. (Original post by Skycat)
Hey all, I'm stuck on the following question:

"A particle has an initial velocity of i + 2j and is accelerating in the direction i + j. If the magnitude of the acceleration is 5 root 2, find the velocity vector and the speed of the particle after 2 seconds."

IF you'd been told the acceleration was i +j, THEN you'd know it's magnitude was , by using pythagoras (draw a diagram if you're uncertain).

BUT you're told the DIRECTION vector for the aceleration is i+j, so you need to scale that direction vector so that it has the correct magnitude to represent the acceleration.

Since the magnitude of the acceleration is and the magnitude of the direction vector is then it's been scaled by a factor of 5.

So the acceleration vector is 5 times the direction vector, i.e. 5(i+j), or 5i + 5j

Hope that helps and that you can take it from there.

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Updated: September 28, 2010
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