How come this solution doesn't include direction for average velocity since it is a vector?
Calculate the average velocity at a particular time interval of a particle if it is moves 5 m at 2 s and 15 m at 4s along x-axis?
Shouldn't average velocity (a vector) be denoted $\vec{V_{av}}$ and it should equal $5\hat{i}$ m/s?
Edit 1:
Best Answer
It is not so, as this particular problem has already somewhat defined the setting that they take velocities along the line of the x-axis hence the solution is consistent with the system taken here and vectors aren’t needed to complicate the result. Indeed using $5i$ would be just as accurate if the question had defined a unit vector along the x-axis as $i$.
Physicists and mathematicians often want to simplify problems if they can afford it without bringing much inaccuracies as it is done here. As here notice that there is no motion along the y-axis. Hence there is really no need for a two-dimensional analysis. This is often done to simplify problems without being unnecessary redundancies which would just mean extra writing. However if the problem did indeed have both x and y movements then it would indeed be very useful to use $i$ and $j$ after defining them.