S = (2 m/s)t + (6 m/s^2)t^2 from t = 0 to t = 4 sec. What shape is this graph? H
ID: 1417767 • Letter: S
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S = (2 m/s)t + (6 m/s^2)t^2 from t = 0 to t = 4 sec. What shape is this graph? How far does the object go between t = 0 & t = 2 sec.? How far does the object go between t = 0 & t = 4 sec ? Is the velocity of the object constant? INTERPRETING GRAPHS It is also important to be able to interpret graphs. For the following graphs, study the graph and answer the questions. Is this object in uniform or accelerated motion?___________. How can you tell? What is the velocity of the object?___________Write the equation for a in terms of t. Describe a physical situation that this graph could depict. PLOTTING GRAPHS If an object is in uniform motion its velocity is constant, for example v = 6 m/s Plot the equation v = 6 m/s from t = 0 to t = 10 sec. (Remember v is on the on the horizontal axis.) What is the v-intercept? (Include units)________This horizontal line tells us the velocity at any time is 6 m/s. The displacement of the above object is found from s = vt Since v = 6m/s this equation is written s = (6m/s)t. Plot this equation from t = 0 to t = 10 sec. For this interval, what is the vertical change in the line (the rise)?________For the same interval what is the horizontal change in the line (the run)?_________What is the slope of the line (including units)?___________. Now look at the equation again. The coefficient of t is also the slope. Do both answers for slope agree? (They'd better.) Objects in accelerated notion are much more interesting. At any given time the velocity of a uniformly accelerating object is found from v = v_0 + at. Plot the equation v = 3m/s + (2m/s^2)t from t = 0 to t = 10 sec. Note the units are included in the formula. They must be part of the graph. What is the y-intercept? (Include units).__________What is the initial velocity of the object?_________. What is the slope between t = 0 and t = 3 sec?__________What is the slope between t = 4sec and t = 6 sec? Is the acceleration of the object constant?___________. What is the acceleration of the object?______________. The equation s = v_0t +1/2at^2 Shows how the position or displacement of an object changes with respect to time, equation:Explanation / Answer
1) Graph is a horizontal line on y axis .
=> v intercept = 6 m/sec
2) Graph is linear line starting from origin with slope of 45 degree .
vertical change in line = 6
horizontal change in line = 1
=> slope of line = 6 m/sec
3) y intercept = 3 m/sec
initial velocity = 3 m/sec
slope = 2 m/sec2
slope = 2 m/sec2
Yes, the acceleration of object is constant .
=> acceleration of object = 2 m/sec2
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