PHY 231
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An automobile rolls 10 meters down a constant incline with slope .05 in 8 seconds, starting from rest. The same automobile requires 5 seconds to roll the same distance down an incline with slope .10, again starting from rest.
• At what average rate is the automobile's acceleration changing with respect to the slope of the incline?
answer/question/discussion: ->->->->->->->->->->->-> :
First Trial:
vAve = 10 meters /8 seconds = 1.25 meters/ second
Initial Velocity assumed to be 0 m/s. Thus, Final Velocity is 2.5 m/s.
a = (( 2.5 m/s - 0 m/s ) / 8 s ) = .3125 m/s/s
Second Trial:
vAve = 10 meters/5 seconds = 2 meters/ second
Initial Velocity assumed to be 0 m/s. Thus, Final Velocity is 4 m/s.
a = (( 4 m/s - 0 m/s ) / 5 s ) = .8 m/s/s
Acceleration / Slope
( .8 m/s/s - .3125 m/s/s ) / ( .10 - .05 ) = 9.75 m/s/s / slope
With respect to the slope of the line, the average rate at which the automobile's acceleration changes is 9.75 m/s/s.
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