Suppose a particle of mass 1 kg is initially at (1, 0, 0) and with initial
velocity ˆ−j +2ˆk and moves under a constant force F = −i +2ˆj. Find
the position and velocity for all time.
The Equation of motion ma = F implies that,
a = −i +2ˆj
which gives the three scalar equations:
integrating for x yields:
x = −1/2t^2+1
integrating for y yields:
y = t^2− t
I am unable find z, where:
d^2z/dt^2 = 0
I need to integrate this equation twice to obtain:
z = 2t
But as far as i understand integrating 0 yields 0. I have a feeling that I'm overlooking something simple but at present it is escaping me and i cannot figure out how to arrive at the given value.
Any help or advice would be greatly appreciated as I am finding this area of Applied math confusing.