91Ó°ÊÓ

The given information can be listed as follows:

• The initial position vector is,m .
• The average velocity is,m/s .
• The initial time is,$t_i=9.0$s .
• The final time is,$t_f=9.7$s .

Average velocity is the ratio of an object’s displacement and time taken.

It can be expressed as follows:

${\stackrel{→}{V}}_{avg}=\frac{{\stackrel{→}{r}}_f-{\stackrel{→}{r}}_i}{t_f-t_i}$

Here,${\stackrel{→}{r}}_f$and${\stackrel{→}{r}}_i$are final and initial position vectors;and are final $t_f$and $t_i$the initial time.

From the formula of average velocity, ${\stackrel{→}{r}}_f$can be derived as follows:

role="math" localid="1653479554793" ${\stackrel{→}{r}}_f={\stackrel{→}{r}}_i+{\stackrel{→}{V}}_{avg}\left(t_f-t_i\right)$.

Substitute the value of ${\stackrel{→}{r}}_i$, ${\stackrel{→}{V}}_{avg}$, $t_i$, and into the equation role="math" localid="1653480484382" ${\stackrel{→}{r}}_f={\stackrel{→}{r}}_i+{\stackrel{→}{V}}_{avg}\left(t_f-t_i\right)$.

role="math" localid="1653480553527"

Hence, the final position of the proton is.