A cyclist starts from home and rides back and forth along a straight east-west r

Question

A cyclist starts from home and rides back and forth along a straight east-west road. Her velocity is given by the figure below (positive velocities = travel toward the east: negative velocities = travel toward the west). Velocity is measured in m/s and time is measured in minutes. (Plot scale: vertical gridlines are spaced 2 units apart: horizontal gridlines are spaced 5 units apart, so the range of the function is [-9, 9] and its domain is [0, 11].) a. On what time intervals is she stopped? b. How far from home is she the first time she stops, and in what direction? c. At what time does she bike past her house? d. If she maintains her velocity at t = 11, how long will it take her to get back home?

Explanation / Answer

From the given question,

a) She has stopped between 1<t<2, 3<t<5 and 9<t<10 where t is in minutes.

b)distance travelled in first 3 min

=[(1/2)(1+3)9]*60

=1080 m

She was 1080 m from her home in east direction.

c)distance covered between 5<t<6 min=(1/2)(1)(9)*60=270m

distance from house= 1080-270=810m

Time it takes= 810/(9)=90 sec=1.5 min

Her bike pasts her home at t=7.5

d)distance covered from east to west= [(1/2)(4+2)(9)]*60

=1620 m

Net distance from home= 1620-1080

=540 m

speed at t=11 min = 9 m/s

time taken to return back= 540/9

=60 sec

=1 minute.

It will take one minute for her to return back.

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