Physics PHY-H110 UNIFORMLY ACCELERATED MOTION OBJECTIVES: (1) Apply the laws of motion to a steel ball rolling down an inclined plane. (2) Determine the average acceleration of the rolling ball. (3) Calculate the % coefficient of variation of the acceleration values for the intervals (4) Plot graphs of distance vs time, final velocity vs time, acceleration vs time. MATERIALS/EQUIPMENT: steel ball, meter stick, trough (inclined plane), ring stand & clamp BACKGROUND: class text book or internet. PROCEDURE: (1) Mark off the trough into 10cm increments. (2) Set up the inclined plane with one end 5 - 8 cm higher than the other end. Secure the ramp so that it won't move. (3) Place the ball on the starting point (0 cm) and release it. Don't push the ball down the incline. Record the time it takes to roll 10cm. (4) Replace the ball on the starting point. Release it and record the time it takes to roll 20cm. (5) Repeat this procedure for 30, 40...... 100cm. (6) Plot distance (s) vs time (t), final velocity (vf) vs time and acceleration (an) vs time (t) DATA: (and Results) distance (d) time (1) time (2) time (3) Time (avg) avg velocity (vavg) final velocity vf) acceleration (an) 0cm 0 0 0 0 0 0 ----------------- 10cm 0.33 0.61 0.56 0.5 20 40 80 20cm 0.58 0.61 0.49 0.56 35 70 125 30cm 0.58 0.78 0.91 0.76 39 78 102 40cm 0.67 0.83 0.81 0.77 52 104 132 50cm 0.67 0.98 1.03 0.89 56 112 126 60cm 0.86 1,11 1.05 1.01 59 118 118 70cm 1.18 1.23 1.25 1.22 57 114 93 80cm 1.08 1.30 1.38 1.25 64 128 102 90cm 1.38 1.45 1.35 1.39 65 130 94 100cm 1.41 1.48 1.56 1.48 68 136 91 acceleration avg _108.1______ std dev ___16.89*__ CALCULATIONS: vavg = d / t vf = 2 x vavg an = ( vf - vo ) / t (1) Plot distance (d) vs time (t), final velocity (vf) vs time and acceleration (an) vs time (t) (2) Obtain average and standard deviation for the acceleration using your calculator's statistical functions (3) Calculate the % coefficient of variation = (std dev / average ) x 100 RESULTS: plot (on a separate page) graphs as described above average acceleration aavg = __108.1___ % coefficient of variation = ____________
As given in part three of the question, divide the standard deviation by the average then multiply by 100.
SOURCE: Please help plotting graphs on TI-83 plus
I believe I already showed you with a profusion of details how to graph functions on the calculator. It would very kind of you to refer to the post that answered your question, so as not to make us answer it all over again. Much appreciated.
Read the following to use the intersection function.
Here are some screen captures
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SOURCE: TI-83 graph problems-help please.
Parabolas
Open Y= editor and type in the two functions
The calculaus functions are accessible by pressing [2nd][TRACE] to open the CALCulate menu options. For the gradient (I think you mean the derivative) use option 6:dy/dx. But first choose the point where you want it calculated (use cursor to move along the curve) and press ENTER. The value of the deivative will be calculated at the chosen point. 
The vertex of the parabolas are maxima. Thus you must use option 4:maximum
You will be prompted for a left bound. Move cursor to the left of the maximum (not too far) and press [ENTER]. A fat arrow is displayed on the graph that shows the left limit of the interval. You will be prompted for a right bound. Move cursor along the curve to the right of the the vertex. Press ENTER. A seconf fat arrow will be displayed to show the right limit of the interval.
You will be prompted for a guess of the maximum. Move cursor newar the max or enter a numerical value and press ENTER.
The location of the vertex is displayed (X and Y values)
I have no idea what you mean by the equation of symmetry
Intercept.
SOURCE: when i press the Y function of my calculator
1. Press up or down arrow to move the cursor to the line of the setting that you want to change.
2. Press left or right arrow to move the cursor to the setting you want.
3. Press enter.
Using sigma notation, and factorials for the combinatorial numbers, here is the binomial theorem:
The summation sign is the general term. Each term in the sum will look like that as you will see on my calculator display. Tthe first term having k = 0; then k = 1, k = 2, and so on, up to k = n.
Notice that the sum of the exponents (n ? k) + k, always equals n.
The summation being preformed on the Ti 89. The actual summation was preformed earlier. I just wanted to show the symbolic value of (n) in both calculations. All I need to do is drop the summation sign to the actual calculation and, fill in the term value (k), for each binomial coefficient.
This is the zero th term. x^6, when k=0. Notice how easy the calculations will be. All I'm doing is adding 1 to the value of k.
This is the first term or, first coefficient 6*x^5*y, when k=1.
Solution so far = x^6+6*x^5*y
This is the 2nd term or, 2nd coefficient 15*x^4*y^2, when k=2.
Solution so far = x^6+6*x^5*y+15*x^4*y^2
This is the 3rd term or, 3rd coefficient 20*x^3*y^3, when k=3.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3
This is the 4th term or, 4th coefficient 15*x^2*y^4, when k=4.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4
This is the 5th term or, 5th coefficient 6*x*y^5, when k=5.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4+6*x*y^5
This is the 6th term or, 6th coefficient y^6, when k=6.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4+6*x*y^5+y^6
Putting the coefficients together was equal or, the same as for when I used the expand command on the Ti 89.
binomial coefficient (n over k) for (x+y)^6
x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4+6*x*y^5+y^6
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