Motion on an inclined plane

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The force that makes the box slide downwards is the component of the gravitational force that is parallel to the incline.

Therefore:

The acceleration of the box can be obtained using Newton's second law:

An accelerating object's position (x) as a function of time (t) is:

Where x0 and v0 are the initial position and velocity respectively. Setting the initial point (A) as x0=0, and since the block starts from rest (v0=0) the equation becomes:

Solving for t:

Thus the time the box needs to get from point A to B (distance b) is:

The time the box needs to get from point A to C (distance c) is:

The time the box needs to get from point A to D (distance d) is:

Setting

We get:

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