A company has budgeted 5 1/4 hours to complete a project, with 1/3 of the time spent on research. How much time does the company plan to spend on research? Express your answer as a mixed number.
To find the time the company plans to spend on research, we need to multiply the total budgeted time by the fraction of time spent on research. To do this, we multiply $5\frac{1}{4}$ by $\frac{1}{3}$. We can convert $5\frac{1}{4}$ to an improper fraction first, \begin{align*}
5\frac{1}{4} &= \frac{5}{1}+\frac{1}{4} \\
&= \frac{5}{1}+\frac{1}{4}(1)\\
&= \frac{5}{1} + \frac{1}{4}\cdot\frac{4}{4}\\
&= \frac{5}{1} + \frac{4}{4}\\
&= \frac{5}{1}+\frac{4}{4}\\
&= \frac{5}{1}+\frac{1}{1}\\
&= \frac{5+1}{1}\\
&= \frac{6}{1}\\
&= 6.
\end{align*}Now that we have $6$ hours as an improper fraction, we multiply $\frac{6}{1}$ by $\frac{1}{3}$: \[
\frac{6}{1}\cdot\frac{1}{3}=\frac{6}{3}=\boxed{2}.
\] Our answer that the company plans to spend $\boxed{2}$ hours on research.