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Seed 7.2
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?
• vAve = `ds/ `dt
• vAve = 10 meters/ 8 sec
• vAve = 1.25 meters/sec
• vAve = 10 meters/ 5 sec
• vAve = 2 meters/ sec
• `dv = .75 meters/sec
You need to calculate the average acceleration on each ramp. `dv and `dt apply to an interval (e.g., the motion down a single ramp), not to results obtained on two different intervals (e.g., not to results obtained for motion down two different ramps, which would involve two completely separate intervals).
• aAve = `dv/ `dt
This is the correct definition, but it applies to only one interval. This definition can be applied to motion on the first ramp to find the acceleration on that ramp. It can then be applied to motion on the second ramp, and if used correctly will give you the acceleration on that ramp.
• aAve = .75m/s / 3 sec
• aAve = .25 meters/sec^2
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15 minutes
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