ch07-p039 - have a velocity vector pointing in the + x...

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39. (a) We first multiply the vertical axis by the mass, so that it becomes a graph of the applied force. Now, adding the triangular and rectangular “areas” in the graph (for 0 x 4) gives 42 J for the work done. (b) Counting the “areas” under the axis as negative contributions, we find (for 0 x 7) the work to be 30 J at x = 7.0 m. (c) And at x = 9.0 m, the work is 12 J. (d) Eq. 7-10 (along with Eq. 7-1) leads to speed v = 6.5 m/s at x = 4.0 m. Returning to the original graph (where a was plotted) we note that (since it started from rest) it has received acceleration(s) (up to this point) only in the + x direction and consequently must
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Unformatted text preview: have a velocity vector pointing in the + x direction at x = 4.0 m. (e) Now, using the result of part (b) and Eq. 7-10 (along with Eq. 7-1) we find the speed is 5.5 m/s at x = 7.0 m. Although it has experienced some deceleration during the 0 x 7 interval, its velocity vector still points in the + x direction. (f) Finally, using the result of part (c) and Eq. 7-10 (along with Eq. 7-1) we find its speed v = 3.5 m/s at x = 9.0 m. It certainly has experienced a significant amount of deceleration during the 0 x 9 interval; nonetheless, its velocity vector still points in the + x direction....
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