Assume that the velocity is a linear function of time, so that
v(t) = a + bt
where
v = velocity (km/h) at time t (hours),
a and b are constants.
When t = 2 hours, v = 18 km/h, therefore
a + 2b = 18 (1)
When t = 4 hours, v = 4 km/h, therefore
a + 4b = 4 (2)
Subtract (1) from (2) to obtain
a + 4b - (a + 2b) = 4 - 18
2b = -14
b = -7
From (1), obtain
a = 18 - 2b = 18 - 2*(-7) = 32
Part A.
The equation is
v = 32 - 7t
Part B
To graph the equation for the first 8 hours, create a table as shown below.
t, hours: 0 1 2 3 4 5 6 7 8
v, km/h: 32 25 18 11 4 -3 -10 -17 -24
We can see from the table that the velocity becomes negative between t=4 and t=5. Therefore, we shall change all negative velocities to zero, and assume that the cyclist comes to rest.
TNote that when the velocity is zero,
32 - 7t = 0
7t = 32
t = 4.57
The new table becomes
t: 0 1 2 3 4 4.57 5 6 7 8
v: 32 25 18 11 4 0 0 0 0 0
The graph is shown below.
