Question

Determine r(t) explicitly from the conditions given below:
r’’(t)=2t^2i+〖te〗^tj-√tk, r’(4)=-i+5j+k, and r(0)4i+4j+k
Determine r(t) explicitly from the conditions given below:
r’’(t)=2t^2i+〖te〗^tj-√tk, r’(4)=-i+5j+k, and r(0)4i+4j+k
@Mathematics

Answer 1

Heres my thinking:
integrate r'' to r' then use r'(4)=-i+5j+k to find the constants in r

Answer 2

Then integrate r' to r and use r(0)4i+4j+k to find constants in r

Answer 3

the j component is te^t

Answer 4

The way I would find the constants are the by setting the integrated function component to the component result in the r''(4) and substituting 4 for t in the integrated function component

Answer 5

Like so: Integrate r’’(t): ∫2t^2 i+te^t j-√t k = 2/3 t^3+c_1i+e^t(t-1)*+c_2j+2/3 t^(3/2)+c_3k

Answer 6

-Use r’(4)=-i+5j+k to find constants:
i: 2/3 (4)^3+c_1=-1 ->128/3+c_1=-1->c_1=-131/3

Answer 7

The reason i am questioning my methodology is cause im getting ugly numbers for c

Answer 8

your idea sounds fine.