# Thread: Mechanics Problem 2 - Vectors

1. ## Mechanics Problem 2 - Vectors

A particle has an intial 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.

Im completely stuck and don't know where to start!! Thanks for your help.

2. Originally Posted by MingMing
A particle has an intial 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.

Im completely stuck and don't know where to start!! Thanks for your help.
Since you know the direction of the acceleration you know that

$\displaystyle \mathbf{a}=s(\mathbf{i}+\mathbf{j})$ but you also know that

$\displaystyle \sqrt{\mathbf{a} \cdot \mathbf{a}}=5\sqrt{2}=\sqrt{2s^2}=|s|\sqrt{2} \implies s=5$

This gives the acceleration vector as

$\displaystyle \mathbf{a}=5\mathbf{i}+5\mathbf{j}$

Can you finish from here?

3. Originally Posted by MingMing
A particle has an intial 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.

Im completely stuck and don't know where to start!! Thanks for your help.
Similar to your other problem $\displaystyle \displaystyle \vec{v} = \vec{v_0} + \vec{a}t$

The acceleration vector will be the unit vector in the direction of i + j times its magnitude.

-Dan

4. Originally Posted by TheEmptySet
$\displaystyle \mathbf{a}=5\mathbf{i}+5\mathbf{j}$
For the record, this is not the acceleration. This is $\displaystyle \displaystyle \vec{a}t$. (Which, of course, you can use as well. )

-Dan

5. Got it