Reviewing for a midterm. I have this problem I can't seem to nail. Want to try it?
"The acceleration of a particle moving only in a horizontal xy-plane is given by a=<(3t)i,(4t)j>, where 'a' is in m/s^2 and 't' is in seconds. At t=0, the position vector r=<(20)i,(40)j> locates the particle which then has the velocity vector v=<(5)i,(2)j>. At t=4s, what is the particle's position vector in unit-vector notation?"
to clarify units: v is in m/s, a is in m/s^2, position is in meters.
The standard kinematics equations, I'm assuming. If calc is involved, I wouldn't know where to implement it.
The Attempt at a Solution
I think it's the acceleration at t=4 seconds that's tripping me up. When I plug in for position in the 'x' or 'y' direction I am using t=4 to multiply with the original acceleration components. Am I not finding acceleration correctly? And wouldn't it stand that if I multiplied an acceleration component by a time I would get a velocity?