Hypothesis: As slope increases, acceleration increases.
Introduction: Speed is the distance traveled per unit time, velocity at any given moment is the slope of the tangent line through any relevant point on the graph, acceleration is the rate at which an object changes its velocity, and instantaneous acceleration is acceleration at any particular instant of time or the limiting value ∆v/∆t as the time interval (∆t) gets vanishingly small.

Speed Formula Velocity Formula Acceleration Formula (also Instantaneous)
Ave. speed= distance Ave. velocity=∆position=displacement Ave. a= ∆velocity=vf-vi
      time time time time time

(Ex. 1) How to convert velocity to speed:




Procedure: see lab book

Incline     Trial     T     t-photo     Vf     a     Ave-a
Low     1     2.10s     0.203705s     0.118m/s     0.056 m/s2     0.050 m/s2
     2     2.04s     0.246067s     0.098m/s     0.048 m/s2     
     3     2.09s     0.249254s     0.096m/s     0.046 m/s2     
Med     1     1.47s     0.139180s     0.172m/s     0.117 m/s2     0.118 m/s2
     2     1.41s     0.141523s     0.170m/s     0.121 m/s2     
     3     1.42s     0.146681s     0.164m/s     0.115 m/s2     
High     1     1.14s     0.114835s     0.209m/s     0.183 m/s2     0.181 m/s2
     2     1.15s     0.110380s     0.217m/s     0.189 m/s2     
     3     1.19s     0.116921s     0.205m/s     0.172 m/s2     
d-card: 0.024 m
Data:












Graphs:


      .250
                         

      .200

Vf
(m/s)      .150


      .100


      0     
           1.00 1.50 2.00 2.50

                     T (seconds)
Sample calculations:







Conclusion: I was successful in proving that as slope increases, acceleration increases.

Analysis: One source of error comes from the slight time delay in human reaction initiation when using a stopwatch to time the car as it rolls down the ramp. This can have a small effect on calculations, so someone more alert should operate the stopwatch. Another error can occur when the photogate gives the wrong calculations. This can happen if a sufficient area of the card on top of the car doesn’t pass through the photogate. Angle and position the photogate so enough area of the card passes through it.