Question

A bicyclist pedals along a straight road with velocity, v, given in the figure below. She starts 7 miles from a lake; positive velocities take her away from the lake and negative velocities take her toward the lake.

http://www.webassign.net/hgmcalc/5-3-26fig.gif

When is the cyclist farthest from the lake?
t = 1 hours (i got this part)

Approximately how far away is she at this time? Give a best estimate. (Round your answer to the nearest whole number.)


miles

Answer 1

The distance traveled from the starting point is given by the area under the velocity graph. The area under the x-axis is calculated as negative area, and positive above the x axis. In this case, we will have to do approximation for the area under the graph. I like thinking in terms of boxes first, and I'd say the first 20 minutes, we have about 1 full negative box, then 7 full positive boxes from 20 mins to 1 hour. Boxes=7-1=6. So distance from lake at t=1 hour is 7miles+6boxes*areaOfABox; where areaOfABox=10*1/6.

Answer 2

thanks