# Homework Help: Kinetic energy

1. Jun 12, 2008

### suppy123

1. The problem statement, all variables and given/known data
A 3.00kg object has velocity 7.00j m/s. Then, a total force 12.0i N acts on the object for 5.00s.
Find the final kinetic energy from 1/2mvf^2 = 1/2mvf . vf

2. Relevant equations

3. The attempt at a solution
i got 1/2 * 3 * (20i+7j)(20i+7j)
then 600j^2 + 210ij + 73.5j^2

but the answer is 673.5 J, why?
since j.j =i.i=1 and i.j=0?

Last edited: Jun 12, 2008
2. Jun 12, 2008

### Kurdt

Staff Emeritus
3. Jun 12, 2008

### suppy123

!? do i need to write the whole of that!!??

600j^2 + 210ij + 73.5j^2
600j.j + 210 i . j + 73.5j.j
600(1) + 210 (0) + 73.5(1)
is this alright

4. Jun 13, 2008

### Kurdt

Staff Emeritus
No thats not how a dot product works. You don't expand the brackets.

$$\mathbf{a} \cdot \mathbf{b} = a_xb_x + a_yb_y$$

For vectors:

$$\mathbf{a} = (a_x,a_y)$$
$$\mathbf{b} = (b_x,b_y)$$

5. Jun 13, 2008

### suppy123

got it, a.b = axbx+ayby
a.b= 20i*20i+7j*7j= 449

Last edited: Jun 13, 2008
6. Jun 13, 2008

### Kurdt

Staff Emeritus
A dot product gives a scalar answer and thats why it is sometimes called a scalar product. Drop the i's and j's and add the numbers together.