Question

Eric is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After three 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 runner 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 5 hours? (5 points)

Answer 1

From the information, it seems the runner is slowing down because the speed at 1st hour is 5km/h but at 3rd hour become 3km/h.

If v= velocity, v0= initial speed, t= time, and the a=acceleration then the function would be: 
v= v0 + a * t

To find the acceleration you need to do this equation:
acceleration= velocity1- velocity3 / t3-t1
a = (3km/h-5km/h)/ (3 hour- 1 hour)
a = (-2km/h)/2hour= -1 km/hour^2

After that you need to find the initial speed. Try to put the 1st hour variable into the full equation. It would look like this
v= v0 + a * t
5km/h= v0 + (-1 km/hour^2 * 1 hour)
v0= 5km/h + 1km/h
v0= 6km/h 

Then the full function would be:
v= 6km/h - 1km/h^2 * t

The graph would look like a backslash(\) from 5 gradually go down to 1. 
6                          
5 O                   
4      O                
3          O             
2              O            
1                   O     
    1   2  3  4  5