Let
y ----> speed in km/h
x ----> time in seconds
we have the ordered pairs
(0,0)
(3,18)
(6,35)
(9,50)
(12,50)
(15,34)
(18,17)
(21,0)
Using a graphing toll
plot the given points
see the attached figure
Estimate the distance traveled
Remember that
the distance is equal to multiply the speed by the time
so
Find out the area of the graph
between interval [0,9] -----> we have a triangle
between interval [9,12] ----> we have a rectangle
between interval [12,21] ----> we have a triangle
step 1
Find out the area of the triangle interval [0,9]
A=(1/2)(b)(h)
where
h=50 km/h----> convert to km/sec----> 50/3,600 km/sec
b=12 sec
A=(1/2)(12)(50/3,600)
A=0.0833 km----------> 83.33 m
step 2
Find out the area of the rectangle interval [9,12]
A=b*h
where
b=12-9=3 sec
h=50 km/h----> convert to km/sec----> 50/3,600 km/sec
A=3(50/3,600)
A=0.0417 km --------> 41.67 m
step 3
Find out the area of the triangle interval [12,21]
A=(1/2)(b)(h)
where
b=21-12=9 sec
h=50 km/h----> convert to km/sec----> 50/3,600 km/sec
A=(1/2)(9)(50/3,600)
A=0.0625 km ------------> 62.5 m
therefore
the total distance is
83.33+41.67+62.5=187.5 m
therefore
the answer is the third option