Questions 19 and 20 refer to the following information
A particle of mass 2.00 \mathrm{~kg} moves under a force given by
\overrightarrow{\mathbf{F}}=-(8.00 \mathrm{~N} / \mathrm{m})(x \hat{\mathbf{i}}+y \hat{\mathbf{j}})
where \hat{\mathbf{i}} and \hat{\mathbf{j}} are unit vectors in the x and y directions. The particle is placed at the origin with an initial velocity \overrightarrow{\mathbf{v}}=(3.00 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(4.00 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}.
After how much time will the particle first return to the origin?
Answer Choices
A. 0.785 \mathrm{~s}
B. 1.26 \mathrm{~s}
C. 1.57 \mathrm{~s}
D. 2.00 \mathrm{~s}
E. 3.14 \mathrm{~s}