We are given graph of position of a person
For finding velocity , we will have to find slope of the given curve
Since, we have to find average velocity between t=6s to t=10s
We can see that there are shape of curve between t=6 and t=10
t=6 to t=8:
There is a inclined line
we can select any two points on that line and find slope
(5,1) and (8,6)
now, we can find slope using formula
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%20m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%20)
now, we can plug values
![m=\frac{6-1}{8-5}](https://tex.z-dn.net/?f=%20m%3D%5Cfrac%7B6-1%7D%7B8-5%7D%20%20)
![m=\frac{5}{3}](https://tex.z-dn.net/?f=%20m%3D%5Cfrac%7B5%7D%7B3%7D%20%20)
so, first velocity is
![v_1=\frac{5}{3} m/s](https://tex.z-dn.net/?f=%20v_1%3D%5Cfrac%7B5%7D%7B3%7D%20m%2Fs%20%20)
t=8 to 10:
We can see that there is horizontal line
so, we can select any two points
(8,6) and (10,6)
now, we can find slope using formula
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%20m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%20)
now, we can plug values
![m=\frac{6-6}{10-8}](https://tex.z-dn.net/?f=%20m%3D%5Cfrac%7B6-6%7D%7B10-8%7D%20%20)
![m=0](https://tex.z-dn.net/?f=%20m%3D0%20%20)
so,
![v_2=0m/s](https://tex.z-dn.net/?f=%20v_2%3D0m%2Fs%20%20)
Average velocity between t=6 and t=10:
now, we can find average velocity
![v=\frac{v_1+v_2}{2}](https://tex.z-dn.net/?f=%20v%3D%5Cfrac%7Bv_1%2Bv_2%7D%7B2%7D%20%20)
![v=\frac{\frac{5}{3}+0}{2}](https://tex.z-dn.net/?f=%20v%3D%5Cfrac%7B%5Cfrac%7B5%7D%7B3%7D%2B0%7D%7B2%7D%20%20)
![v=0.8](https://tex.z-dn.net/?f=%20v%3D0.8%20%20)
so,
average velocity is 0.8m/s...........Answer