A continuous curve that shows an object\'s position as a function of time is cal

Question

A continuous curve that shows an object's position as a function of time is called a position-versus-time graph. You can gain relevant information on an object's motion if you interpret such graphs correctly. To do that, it is useful to review the definition of velocity. For motion along a line, the velocity v_x is the ratio of the displacement Delta x of an object to the time interval Delta t during which this displacement occurs, which can be written as v_x = Delta x/Delta t. This equation has a graphical interpretation: It tells us that v_x is the slope of the position-versus-time graph representing the motion. This implies that you can associate the slope of the graph, a geometrical quantity, with the physical quantity velocity. This and other aspects of interpreting position-versus-time graphs are outlined in Find the object's positions x_1, x_2, x_3, and x_4 at times t_1 = 2.0 s, t_2 = 4.0 s, t_3 13 s, and t_4 = 17 s. Express your answers in meters to one significant figures, separated by commas. x_1, x_2, x_3, x_4 = m, m, m, m Find the object's speeds v_1, v_2, and v_3 at times t_1 = 2.0 s, t_2 = 4.0 s, and t_3 = 13 s. Express your answers in meters per second to two significant figures, separated by commas. v_1, v_2, v_3 = m/s, m/s, m/s

Explanation / Answer

A)
General equation of a straight line is x = x0 + vt
Where xo is the y-axis intercept and v is the slope of the straight line.
i) t = 2 s
Velocity during 0 to 3 s, v1 = (7-0) / (3 -0) = 2.33 m/s
Here xo = 0
Position at t = 2 s, x = 0 + 2.33 x 2
= 4.66 m.
ii) t = 4 s
Here xo = 7 and v = (7 - 7) / (6 - 3) = 0
x = xo + 0
= 7 m
iii) t = 13 s
Consider the time interval from 11 to 16 s.
Slope of the curve, v = (7 - 10) / (16 - 11) = - 0.6 m/s
At t = 11 s, x = 10 m
10 = xo + (-0.6) x 11
xo = 10 + 6.6 = 16.6 m
Position at t = 13 s,
x = 16.6 - 0.6 x 13
= 8.8 m
iv) t = 17 s
position is at the origin, x = 0 m

B)
From the previous part,
v1 = 2.33 m/s
v2 = 0 m/s
v3 = - 0.6 m/s

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