Question

Max is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After two hours, the velocity of the runner is 3 km/h. Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points) Part B: How can you graph the equations obtained in Part A for the first 4 hours? (5 points)

Answer 1

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Explanation:

Answer 2

Given:
Velocity = 5 km/h after 1 hour
Velocity = 3 km/h after 2 hours

Part A.
Let
v = a + bt
where
v = velocity, km/h
t = time, hours

Because v=5 when t=1, therefore
a + b = 5 (1)
Because v=3 when t=2, therefore
a + 2b = 3 (2)
Subtract (1) from (2).
a + 2b - (a + b) = 3 - 5
b = -2
From (1), obtain
a - 2 = 5
a = 7

Answer: v = 7 - 2t

Part B.
To graph the equation for 0<=t<=4, create a table.
t v
--- -----
0 7
1 5
2 3
3 1
4 -1 (gnore negative speed)

The graph is shown below.