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2 Conclusions: If you need help filling in the blanks, use the attached word bank. 1. What conclusions can you make about the graph of the acceleration vs. time for an object that is accelerating at a uniform rate? a. The graph of the acceleration vs. time for an object accelerating at a constant rate is a function (which is graphed as a line) (a degree ). b. The area captured between the time axis and the acceleration vs. time graph can be calculated by multiplying ( units) by ( units), yielding in (units) which can be used to construct the vs. time function. 2. What conclusions can you make about the graph of the velocity vs. time for an object that is accelerating at a uniform rate? a. It is a function (a degree ). b. The is equal to the rate of. c. If the acceleration is negative, the of the velocity vs. time function is. d. If the acceleration is positive, the of the velocity vs. time function is. e. The average value of the velocity vs. time is v avg = v = because. f. The area captured between the time axis and the velocity vs. time graph can be calculated by multiplying ( units) by ( units), yielding in (units) which can be used to construct the vs. time function. g. The slope at any point is equal to the of the object, and is constant.

3 Conclusions (continued): 3. What conclusions can you make about the graph of the position vs. time for an object that is accelerating at a uniform rate? a. It is a function (a degree ). b. If you hold a pencil evenly up against any point on the curve, this represents the of the curve at the point, which has the physical meaning of the at that point in time. c. If the acceleration is negative, the slope of the function as time increases (to see what happens, you can hold a pencil up against the curve to represent the tangent at a point, then move the pencil to the right and watch what happens to the tip of the pencil as you follow the curve the tip of the pencil moves ). In mathematics this property of a curve is commonly known as being or, more accurately, as simply being. d. If the acceleration is positive, the slope of the function as time increases (to see what happens, you can hold a pencil up against the curve to represent the tangent at a point, then move the pencil to the right and watch what happens to the tip of the pencil as you follow the curve the tip of the pencil moves ). In mathematics this property of a curve is commonly known as being or, more accurately, as simply being. e. The slope at any point on the position vs. time function physically represents the of the object at that point in time. f. The area captured between the curve and the time axis has physical meaning. 4. Can you think of any realistic situations for which constant acceleration may be an appropriate physical model? (answer on back) First look up and write down Newton s 2nd law on the back of this page along with the simple equation associated with the law. Typically, the mass of the accelerating object is unchanging (can you think of any examples for which mass changes over time?). If mass is constant, this implies that the and the must be.

4 Word Bank for filling in conclusions: Use all but three of the words below to fill in the shorter blanks. You should fill in an explanation for the longer blanks! acceleration position (x) acceleration positive negative acceleration polynomial polynomial polynomial height tangent linear instantaneous instantaneous height s (seconds) instantaneous zero 1 st 2 nd s (seconds) force no slope slope m/s 2 or ft/s 2 concave negative horizontal length m/s or ft/s concave slope slope decreases m/s or ft/s concave increases length velocity m or ft convex upward downward velocity elephant constant upward downward velocity yak constant quadratic zebra velocity

5 Given: constant positive acceleration a x = +30 ft/s 2, initial position x o = +80 ft, initial velocity v xo = 120 ft/s

6 Given: constant negative acceleration = a x = 10 m/s 2, initial position x o = 20 m, initial velocity v xo = + 40 m/s

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