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1 Name: Date: Honors Physics Worksheet on Position, Velocity, and Acceleration Graphs when acceleration is constant Suppose you have an object that moves with a constant acceleration. Your task is to create accurate acceleration, velocity, and position versus time graphs from this information. Of course, you know from our class discussions that you will also need to know an initial velocity and an initial position to create complete graphs. Here is your starting information ( initial conditions ): Initial Conditions Positive Acceleration Problem Negative Acceleration Problem Position (x o ) + 80 ft -20 m Velocity (v xo ) 120 ft/s + 40 m/s Acceleration (a x ) + 30 ft/s 2 10 m/s 2 1. Using the attached graph paper, draw your acceleration vs. time graph for a period of 6 seconds, starting at t = 0 s. Pick appropriate scales and label your axes, and put a title on the graph. Find the equation for your graph: a x (t) = Type of function: 2. Repeat for your velocity vs. time graph. You ll have to pick a nice scale to fit your data. Find the equation for your graph: v x (t) = Type of function: 3. Repeat for your x-position vs. time graph. You ll have to pick a nice scale to fit your data. Find the equation for your graph: x(t) = Type of function: 4. Looking at you graphs, what is the average value for each of the graphs over the 6- second time interval? Describe how you determined each value: a. average acceleration: b. average velocity: c. average position: 5. Can you see a pattern relating to the three equations you found for 1 3 and the given initial conditions? If you were given x o, v xo, and a x as variables instead of numerical quantities, what would the general equations for a x (t), v x (t), and x(t) look like?

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

If we plot the position of a moving object at increasing time intervals, we get a position time graph. This is sometimes called a distance time graph.

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