Ineed to figure out how to solve this problem and solve !

This is actually more math than physics.

This is a graph of how far a shopper is from where she started, as time goes on.
Every point on the line is a point in time and space:  The number down below it
   shows how long it was after the beginning, and the number to the left of it shows
   the distance from the starting place.

Look along the bottom.  The graph only covers the first 100 seconds.
Look up along the left side.  The graph can only show distance that are
     30 meters or less from where she started.  If she gets farther away,
      the line will go up off the graph.  

Now, here are some things you're going to see on the graph:

-- When she's walking away from the cart pick-up, her distance from it
is increasing as time goes on.  So the line on the graph is rising.

-- When she's standing still in the store, her distance from the cart pick-up
isn't changing as time goes on.  So the line on the graph is flat.

-- When she's walking TOWARD where she started, her distance from it
is decreasing as time goes on.  So the line on the graph is dropping.

-- The faster she walks, the faster the distance changes, so the line is steeper.

Knowing this, you can look at the graph and see what happened:

-- She started some place when Time was zero.
    I call it picking up the shopping cart.

-- In the first 20 seconds, she walked 15 meters away from the carts.

-- Then she stood still for 10 seconds.

-- Then she walked away from the carts, faster, for another 10 seconds.
    Now she was 25 m from them. 

-- Then she stood still again for 10 seconds.

-- Then she turned around and walked back toward the carts for 10 seconds.
    At that time, she was only 20 m from where she started.

-- She stood still there for 10 seconds.

-- She turned again, and resumed walking away from where she started.
   She walked rather slowly for 30 seconds, and wound up 30m from
         where she started, 100 seconds after she left it.

That's all we know, because that's the end of the graph.

The question wants you to describe this motion.
When you write it up, please don't just copy my words.  Make it your own.
  

Centrapedial force is the answer