Mark is observing the velocity of a runner at different times. after one hour, the velocity of the runner is 6 km/h. after three hours, the velocity of the runner is 2 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)

You have only two pair of data:

Time      velocity
hour        km / h

  1              6
  3              2

=> (1, 6), (3, 2)

Given that you have only two points you have to make an assumption to deal with them.

Question 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

1) variables

Independente variable: time =  t
Dependent variable: velocity = v

2) Model: the best assumption that you can make with only two data is that the function follows a linear model, which means that the rate of change of the dependent variable with respect the independent variable is constant.

The rate of change of velocity is acceleration. So, the acceleration is constant. This is, the model assumed is uniformly accelerate motion.

The equation is found as:

  v - 6      2 - 6
=
  t - 1      3 - 1

      v - 6         -4
=> =    = - 2
      t - 1          2

=> v - 6 = - 2 (t - 1)

=> v = -2t + 2 + 6

=> v = -2t + 8

In standard form, that is: v + 2t - 8 =0

Question B: How can you graph the equations obtained in Part A for the first 5 hours? (5 points)

1) vertical axis: time

2) horizontal axis: velocity

3) table:

t          v = -2t + 8
h             km/h

1           6
2          -2(2) + 8 = 4
3          -2(3) + 8 = 2
4          -2(4) + 8 = 0
5          -2(5) + 8 = - 2

4) With that information you can make the graph which is a line.

You can also graph the function using only the two original points, given that two points define a line.