To solve this problem,
we assume that velocity is a linear function of time:<span>
<span>v(t) = m t + b
where
v = velocity</span></span>
t = time
m = slope of line
b = y-intercept of
line equation
When t = 2 hours, v =
18 km/h, therefore:<span>
2 m + b = 18 (1)
When t = 4 hours, v = 4 km/h, therefore
4 m + b = 4 (2)
Subtract (1) from (2) to obtain
4 m – 2 m = 4 - 18
2 m = -14
m = -7
</span>
From (1), calculate
for b:<span>
b = 18 – 2(-7) = 32</span>
<span>
Part A. The
equation in standard form is therefore:
<span>v = -7 t + 32
Part B. To graph
the equation for the first 8 hours, we create a table as shown below. Assign
values of t from 0 to 8 hours then calculate the corresponding velocity.</span></span>
t, hours: 0 1 2 3 4
5 6 7 8<span>
v, km/h: 32 25 18 11 4 -3
-10 -17 -24
<span>From the table, the velocity becomes negative between
t=4 and t=5. This means that between this time, Marion already came to rest.
Note that when the velocity is zero, t is
equivalent to</span>
32 - 7t = 0
7t = 32
t = 4.57
<span>The new table is below and we plot it.
t: 0 1 2 3 4
4.57 5 6 7 8
v: 32 25 18 11 4 0
0 0 0 0
<span> </span></span></span>