Phy 121
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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: in situation 1 vAve = `ds/`dt = 10m/8s = 1.3m/s so vf = vAve*2 = 2.6 so aAve = `dv/`dt = 2.6m/s / 8s = .33m/s^2
In situation 2 vAve = `ds/`dt = 10m/5s = 2m/s so vf = 2*vAve = 2*2m/s =4m/s so aAve = `dv/`dt = 4m/s / 5s = .8m/s^2
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15min
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You still have to calculate the ave rate of change of accel with respect to ramp slope:
The average rate of change of acceleration with respect to ramp slope is
ave rate = change in acceleration / change in ramp slope
= ( .8 m/s^2 - .33 m/s^2) / ( .10 - .05 )
= (.47 m/s^2) / (.05)
= 9.4 m/s^2,
meaning 9.4 m/s^2 per unit of ramp slope.
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