Motion on an inclined plane
Determine the time time tB, tC, and tD needed for a block of mass m to slide from rest at A to points B, C, and D, respectively. Neglect effects of friction.
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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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