Introduction: 

    The purpose of this lab was to determine the motion of a marble sliding down a ramp is uniform or non-uniform.  According to theory, you know an object is accelerating if the shape of the s vs. t graph is non linear.  However, the graph does not tell you if the motion is uniform or non-uniform acceleration.  To know for certain if an object is traveling with uniform acceleration you must look at the velocity vs. time graphs.  

Method:

Results:

Analysis:

Discussion: 

    ¹⁾Based on the results in this lab it would appear that the motion of a ball traveling down an incline is an example of uniform acceleration.

²⁾t = ms^.5 + b ≅ s = V₁t + .5at² 

t = ms^.5 + b

(t - b)² = (ms^.5)² 

t² -2tb + b² = m² s

sm² = -2bt + t² +b² 

.5sm² = -bt + .5t²  + .5b² 

s = V₁t + .5at² 

    Since, t = ms^.5 + b ≅ s = V₁t + .5at² and s = V₁t + .5at²  is one of the formulas derived from a uniform acceleration graph.  Therefore, t = ms^.5 + b is also an equation that can be used to define a graph of constant acceleration.

³⁾ The Derivative of s vs. t form a "linear" relation

    Errors:  The Ramp that was used to guide the marbles path was less than flawless.  Their were areas in the ramps where carpentry nails once were and have left small irregularities in the wood.  These small imperfections in the wood may cause there to be more friction on the path of the marble and alter the results.