Answer:
The average velocity of the particle is [tex]\vec {v}_{avg} = 4\,\hat{i} +24\,\hat{j}\,\left[\frac{m}{s} \right][/tex].
Step-by-step explanation:
In vector terms, the average velocity of a particle ([tex]\vec v_{avg}[/tex]), in meters per second, at a given time change ([tex]\Delta t[/tex]), in seconds:
[tex]\vec v_{med} = \frac{\Delta x}{\Delta t}\,\hat{i} + \frac{\Delta y}{\Delta t}\,\hat{j}[/tex] (1)
Where [tex]\Delta x[/tex] and [tex]\Delta y[/tex] is the change in position for x and y axes, in meters.
[tex]\Delta x = x(2) - x(1)[/tex]
[tex]\Delta x = (4\cdot 2 - 1)-(4\cdot 1 - 1)[/tex]
[tex]\Delta x = 4\,m[/tex]
[tex]\Delta y = y(2) - y(1)[/tex]
[tex]\Delta y = 8\cdot (2)^{2}-8\cdot (1)^{2}[/tex]
[tex]\Delta y = 24\,m[/tex]
[tex]\Delta t = 2\,s - 1\,s[/tex]
[tex]\Delta t = 1\,s[/tex]
[tex]\vec v_{avg} = \left(\frac{4\,m}{1\,s}\right)\,\hat{i} + \left(\frac{24\,m}{1\,s} \right) \,\hat{j}[/tex]
[tex]\vec {v}_{avg} = 4\,\hat{i} +24\,\hat{j}\,\left[\frac{m}{s} \right][/tex]
