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Question 1
Read the scenario carefully
Scenario 1: A runner is racing in a 10-kilometer (km) race. The runner travels the first 2
km in 12 minutes (min). Then the runner stops for 2 min to have a drink of water. He
begins running again, and covers the next kilometer in 5 min. The following 3 km have
the same pace: 6 minutes per kilometer (min/km). The runner again pauses to tie his shoe;
he is paused for 1.5 min. He has 4 remaining km to go. When he starts running again, he
runs 1 km in 5 min, but the remaining 3 km are each 1 min slower than the one before (6
min, 7 min, and 8 min, respectively). Create a distance-time graph to show the runner's
speed
Construct a distance-time graph to show how the object(s) in your scenario move(s) over
time. Remember that the y-axis represents the distance traveled by an object, and the x-
axis represents time. Include the appropriate units on your graph.



Sagot :

The kinematics and the graphical representation allow finding the results for the realization of the graph and the calculation of each speed are:

  • In the attachment we can see the graph of distance versus time
  • The speeds are different in each time interval and are represented by the slope of the graph.

The kinematics analyzes the movement of the bodies to find relationships between the position, the velocity and the acceleration of the bodies, in the special case that the acceleration is zero is called uniform movement and is described by the expression

                   [tex]v = \frac{\Delta x}{t}[/tex]  

Where v is the velocity, Δx the change of position, t the time of the interval

In this exercise they ask for a graph of the position versus time, let's build a table with the data of time and change of position

 

 Time      Δx            Time                 Distance

 (min)     (km)        accumulated    accumulated

                                  (min.)                  (km)

    0          0                  0                         0

   12          2                 12                         2

    2          0                 14                         2

    5           1                 19                        3

   18          3                 37                       6

     1.5       0                38.5                    6

     5          1                43.5                    7

     6          1                49.5                    8

     7          1                56.5                    9

     8          1                64.5                   10

The total distance is the sum of all the distances

           [tex]x_{total}[/tex] = 2 + 1 + 3 +1 + 1 + 1 + 1

           [tex]x_{total}[/tex] = 10 km

Let's find the distance traveled for the intervals where it travels 3 km at 6 min / km, therefore for the three kilometers use a time of 18 min

In the attachment we can see a graph of the accumulate distance on the y axis versus the accumulate  time on the x axis.

In this graph we can calculate that it has several speeds

Let's find the velocities of each interval

Interval 1

         Time 12 min

         v₁ = 2-0 / 12

         v₁ = 0.166 km / min

interval 2 and 5

         Distance Δx = 0

         v₂ = v₅ = 0 km / min

Interval 3

       Time 5 min

         v₃ = 1/5

         v₃ = 0.2 km / min

Interval 4

        Time 18 min

        v₄ = 3/18

        v₄ = 0.166 km / min

interval 6

          time 5 min

          v₆ = 1/5

          v₆ = 0.2 km / min

Interval 7

           Time 6 min

           v₇= 1/6

           v₇ = 0.166 km / min

Interval 8

          Time 7 min

           v₈ = 1/7

           v₈ = 0.143 km / min

Interval 9

       Time 8 min

        v₉ = 1/9

        v₉ = 0.111 km / min

These speed are the slopes of the different lines that are observed in the graph.

In conclusion with kinematics and graphical representation can find the results for the realization of the graph and the calculation of each velocity are:

  • In the attachment we can see the graph of distance versus time
  • The speeds are different in each time interval and are represented by the slope of the graph.

Learn more here: https://brainly.com/question/24194180

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