## Statement

difficulty
A person walks in a straight line at a velocity of 5 km per hour for 15 minutes. Could you determine its graph of position with respect to time?

## Solution

Data

v = 5 km / h = 5000 m / 60 min / h = 83.33 m / min -- Velocity
x0 = 0 m -- Initial position.
t0 = 0 min -- Start time
tf = 15 min -- Final time

Resolution

Since the person walks in a straight line and with constant velocity, we have a uniform rectilinear motion. The position equation for this type of motion is x = x0 + v · t . This way, by applying the formula for the position we can calculate its position, for examples, at four different times like t = 0, 5, 10 and 15 minutes

t x
0 x = 0 + 83.33 · 0 = 0
5 x = 0 + 83.33 · 5 = 416.65
10 x = 0 + 83.33 · 10 = 833.3
15 x = 0 + 83.33 · 15 = 1249.95

To solve the exercise, and for simplicity, you can observe that we have taken meters as unit of position and minutes as unit of time. Then we represent pairs of values obtained from points in a graph where position is given by the x-axis and time by the t-axis.

Notice that we used 4 points to draw the graph although it is enough with only two of them, since a u.r.m. graph is a straight line and a line can be drawn knowing only two of its points.

## Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
Related sections
$x={x}_{0}+v\cdot t$