You are consulting for an elevator company. During a safety test, technicians cr

Question

You are consulting for an elevator company. During a safety test, technicians created the following graph of the velocity of the elevator versus time; you have been asked to interpret the graph. Unfortunately, you are told that the technician who printed the graph has made two mistakes. The labeled interval on the velocity axis should be 2.3 m/s rather than 2.0 m/s, and the labeled time interval should be 3.6 s rather than 4.0 s. You should begin by redrawing the graph on your own paper with the proper labels on the velocity and time axes.

Since this motion is purely one-dimensional, give your answers to the following questions using a coordinate system consisting of a y-axis in the Up-Down direction with Up as positive. Indicate directions by the appropriate plus or minus sign. Assume that the test begins (at time zero) with the elevator at position y0=-3.2 m (i.e. 3.2 meters below ground level -- ground level has been selected as the location at which y=0).

(a) What is the position of the elevator at time 1.8 seconds?
m

(b) What is the position of the elevator at time 7.2 seconds?
m

(c) What is the position of the elevator at time 9 seconds?
m

(d) What is the position of the elevator at time 12.6 seconds?
m

(e) What is the position of the elevator at time 14.4 seconds?
m

(f) What is the position of the elevator at time 16.2 seconds?
m

(g) What is the position of the elevator at time 18 seconds?
m

Explanation / Answer

a) s = -3.2 + 0.5* (1.8*1.8)* (2.3/1.8) = -1.13 m b) s = -1.13 + 5.4*(2.3) = 11.29 m c) s = 11.29 + 2.07 = 13.36 m d) s= 13.36+ 0 = 13.36 m e) s = 13.36 - 2.07 = 11.29 m f) s = 11.29 - (2.3*1.8) = 7.15 m h) s = 7.15 - 2.07 = 5.08 m

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