# Applications of vector algebra to physics

1. Jul 29, 2009

### rugapark

1. The problem statement, all variables and given/known data

A ball of mass 1 kg is acted upon by three forces:
Fl = (2i + 4j - 3k) N, F2 = (-3i - j + 2k) Nand F3 = (i - 5j - k) N.
Determine a vector expression for the acceleration of the particle.
If, at time t = 0, it has position r = (i +j) m and velocity u = (i +3j)m/s, write
down the position vector of the ball at time t. Hence, determine its position and
velocity after 2 seconds.

2. Relevant equations

3. The attempt at a solution

resultant force & acceleration due to forces:

Fresultant = F1+F2+F3 = -(2j+2k)N

F=ma, m=1kg, therefore a = -(2j+2k)ms-2

position vector at (t), and velocity and position at t=2:

r(t)=r(0)+ut+$$\frac{1}{2}$$at2

therefore r(t)=(i+j)+(i+3j)-$$\frac{1}{2}$$(j+k)t2

so at t=2,

r(2)=(3i+5j-2k), and v(2)=(i+j-2k)ms-1

any problems? thanks for all the help always!

2. Jul 29, 2009

### Dick

No conceptual problems. You are being pretty sloppy about putting the numbers into r(t)=r(0)+v(0)*t+(1/2)*a*t^2, though. I'd try that part again.