A particle starts at the initial position r(0)=<0,0,1> with the initial velocity v(0)=<1,0,0> and the accelerlation a(t<sin(t),e^(t),12t>. Find its position function r(t).
Hello, allstar2!
The velocity function is the integral of the acceleration function.
We are told that: .
So we have: .
. . . . . . . . . . . . . .
Then we have: .
Hence: .
The position function is the integral of the velocity function.
We are told: .
So we have: .
. . . . . . . . . . . . . .
Then we have: .
Therefore: .