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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?
10 m/ 8 s = 1.25 m/s
10 m/ 5 s= 2 m/s
2 m/s – 1.25 m/s / 3s = 0.75 m/s / 3 s = 0.25 m/s^2
Right idea, but these two velocities were calculated over different trials, therefore over different time intervals, with a different acceleration on each.
You need to calculate an acceleration for each trial.
If the automobile rolls 10 meters from rest in 8 seconds, then what is its acceleration?
If the automobile rolls 10 meters from rest in 5 seconds, then what is its acceleration?
You have the average velocity for each trial, and you know that the initial velocity for each is 0. What therefore is the acceleration for each?
In terms of the definition of average rate of change of A with respect to B, what is the definition of average rate of change of acceleration with respect to ramp slope?
Using this definition and the information you have at this point, what is this rate?
You made a plausible attempt, but you first need to find an acceleration for each of the two trials.
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