Starting at -12m a person walks in the negative direction for 15 m then turns around and walks 45m in the positive direction. Where is his final position? What was his overall displacement? How much distance did he travel?

We need to define:

When the person walks in the negative direction, we need to subtract the distance walked from the actual position.

When the person walks in the positive direction, we need to add the distance walked to the actual position.

We know that the person starts in the position -12m, then we start with:

Position = -12 m

Then the person walks 15m in the negative direction, then the new position will be:

Position = -12m - 15m = -27m

Now the person walks 45m in the positive direction, then the new position will be:

Position = -27m + 45m = 18m

This is the final position.

Now we want to find the displacement, which is equal to the difference between the final position (18m) and the initial position (-12m)

Then we have:

Displacement = 18m - (-12m) = 18m + 12m = 30m

How much distance he travels?

Here we need to add the absolute value of all the distances that he traveled.

He first traveled 12m and then traveled another 45m

Then the total distance traveled is

Distance traveled = 12m + 45m = 57m