# Solving position vectors using given speed.

1. Sep 3, 2010

### riddle

1. The problem statement, all variables and given/known data
A particle P starts at the point with position vector 4i + j. P moves with constant velocity vm/s. After t seconds, P is at the point with position vector 12i - 11j. Find t if the speed of P is 4m/s.

2. Relevant equations
n/a

3. The attempt at a solution
6i - 3j = -2i + 3j + vt
=> 8i - 6j = vt
=> 8i - 6j = *bleh. and now I'm stuck.*

2. Sep 3, 2010

### Staff: Mentor

Use the formula in the attachment in your other problem, r = r0 + vt.

In your attempt, where did 6i - 3j and -2i + 3j come from? They don't have anything to do with this problem.

At 0 seconds, the particle is at r0 = 4i + j. After t seconds, r = 12i - 11j.

So 12i - 11j = 4i + j + v t.

Start with this equation, simplify it a bit, and use the idea that if two vectors are equal, their magnitudes are also equal.

3. Sep 3, 2010

### riddle

HAHAHAHA. This is the second time I've done this. *facepalm* I copied the wrong vectors.
r0 = -2i + 3j, and r = 6i - 3j.

So, 8i - 6j = tv

And I really have no idea what to do to proceed.

EDIT: Ok. So,
8i - 6j = vt
Both sides are equivalent.
Speed = |v|
So,
| 8i - 6j | = |vt|
=> 10 = 4t
=> t= 2.5
So t=2.5 seconds?
But can you just multiply like that?
What I mean to say is that is |vt| = |v| * t ?

Last edited: Sep 3, 2010
4. Sep 3, 2010

### Staff: Mentor

Both sides are equal. There is a difference. Statements can be equivalent (same truth values); expressions can be equal (or less than, greater than, etc.).
Yes, the magnitude of a scalar times a vector is the scalar times the magnitude of the vector.

More precisely, |kv| = |k||v|. This takes into account the possibility that k is a negative number.

5. Sep 3, 2010

### riddle

Wait, don't you mean |kv| = k * |v|
Or are you just implying that the magnitude of a scalar is the sacalr itself, i.e, |k| = k

*sigh* I need some sleep.

6. Sep 3, 2010

### Rasalhague

|k| means the absolute value of the scalar k, which is always positive, like the magnitude (length) of a vector. So if k = -5, then |k| = 5. If k = 5, |k| = 5. It just means, throw away the minus sign if there is one.

7. Sep 3, 2010

### Staff: Mentor

No, I mean exactly what I wrote, namely that |kv| = |k||v|. The magnitude of a scalar is its distance from 0.

For example, let v = 3i + 4j, so |v| = 5.
|-2v| = |-2(3i + 4j)| = |-6i - 8j)| = $\sqrt$((-6)2 + (-8)2) = $\sqrt$(36 + 64) = $\sqrt$(100) = 10 = 2|v|

8. Sep 3, 2010

### riddle

Oh.
I can't wait till I'm as smart as you guys. *anticipation emoticon*
EDIT: And thanks for all your help.

Last edited: Sep 3, 2010