The middle or centre of the Earth is the core. However the middle of the layers from the surface to the centre of the Earth is known as mantle.
I do not understand the full question, however if you are wondering which way Simone and the dog will go, they will go right because the force of 34 N from the dog is higher than the force of 16 N from Simone.
Answer:
a) 
Now we can replace the velocity for t=1.75 s

For t = 3.0 s we have:

b) 
And we can find the positions for the two times required like this:
And now we can replace and we got:

Explanation:
The particle position is given by:

Part a
In order to find the velocity we need to take the first derivate for the position function like this:

Now we can replace the velocity for t=1.75 s

For t = 3.0 s we have:

Part b
For this case we can find the average velocity with the following formula:

And we can find the positions for the two times required like this:
And now we can replace and we got:

Answer:
20.7 s
Explanation:
The equation to calculate the velocity for a uniform acceleration a, time t and initial velocity v₀:
v = a*t + v₀
Solve for t:
t = (v - v₀)/a