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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: ->->->->->->->->->->->-> :
vAve = ‘ds / ‘dt
vAve = 10m / 8s
vAve = 1.25m/s
v0 = 0m/s
vAve = (v0 + vf) / 2
1.25m/s = (0 + vf) / 2
vf = 2.5m/s
aAve = (vf - v0) / ‘dt
aAve = (2.5m/s - 0m/s) / 8s
aAve = 2.5m/s / 8s
aAve = 0.313m/s^2
vAve = ‘ds / ‘dt
vAve = 10m / 5s
vAve = 2m/s
v0 = 0m/s
vAve = (v0 + vf) / 2
2m/s = (0 + vf) / 2
vf = 4m/s
aAve = (vf - v0) / ‘dt
aAve = (4m/s - 0m/s) / 5s
aAve = 4m/s / 5s
aAve = 0.8m/s^2
average rate = change in acceleration / change in slope
average rate = (.8m/s^2 - .313m/s^2) / (.10 - .05)
average rate = 9.75m/s^2
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&#Your work looks very good. Let me know if you have any questions. &#