Use Hooke's Law and Newton's 2nd Law to derive a formula for the acceleration of an object of mass m on a frictionless surface which is attached to a spring with a constant k which is stretched a distance L. The acceleration should be in terms of m, k, and L.

a = kL/m

Explanation:

Here we can use Hooke's Law to find out the force applied on the system. Hooke's Law states that when a spring is stretched by some force, the force applied is directly proportional to the displacement of spring. The formula is given as:

F = kL

Now, the Newton's Second Law of motion states that whenever an unbalanced force is applied to a body it produces an acceleration in the body, in its own direction. So, the force is given by the formula:

F = ma

Comparing both the forces, we get:

kL = ma

a = kL/m

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)