We want to find and graph the motion equations by finding the ratios.
The graph can be seen at the end of the answer.
We define the rate of change as the rate at which one variable changes with respect to other.
Here, we know that you move 30 meters every 5 seconds, then your rate of change in position is:
r = 30m/5s = 6 m/s
Note that this is a speed.
For your friend, we know that he/she moves 9 meters in 2 seconds, so his/her rate is:
r' = 9m/2s = 4.5 m/s.
Now we need to graph these in a coordinate plane, but these are just numbers, I assume that you want the motion equation graphed.
The motion equations are just given by the rate we just fond times the variable, in this case, the variable is the time in seconds.
Your equation is:
p(t) = (6 m/s)*t
Your friend equation is:
p'(t) = (4.5 m/s)*t
The graphs can be seen below, the green one is the first function, and the blue one is the second.
If you want to learn more, you can read:
