III.1.5. The graphical representation of the movement.

👀 The graphical representation of a mobile movement.

In order to represent the graph of the movement of a mobile (Luiza's running on the 100 m track) the following four steps must be completed:

1) Make a table with the movement data (their corresponding positions and times).

2) Draw the axes, two perpendicular lines, one horizontal and one vertical, on a math sheet or on graph paper. The horizontal axis is called the abscissa axis (Ox) and the vertical axis is called the ordinate axis (Oy). The two axes are graded (calibrated) by choosing a standard for each, so that we can represent all the positions of the mobile and their corresponding moments.

For our example I will choose as a standard (scale):

For the distance axis:
1 cm : 5 m

For the time axis:
1 cm : 1 s.

The point of intersection of the axes is O = the origin for each axis, ie at this point we have 0 m and 0 s.
The abscissa is the axis of time. Note the axis and at its end, write t (s).
The order is the distance axis (the positions of the mobile are noted on this axis). Note the axis and at its end write x (m).

3) Draw each point in the table on the graph.

The first point is right at the origin, O (x₀=0, t₀=0).
To represent the second point, A (x₁ = 25 m, t₁ = 3 s), we proceed as follows: next to the numerical value of 3 s, a vertical line goes, dotted. Next to the numerical value of 25 m, a horizontal line is pointed. The point of intersection of the two dotted lines is the point on the coordinate graph A(x₁, t₁).
Continue with the other three points: B (x₂, t₂), C (x₃, t₃), D(x₄, t₄), according to the model shown above, until all five are plotted points in the table.

4) Draw the graph of the movement by joining all the previously built points.

Remark:

Don't confuse the trajectory of the mobile with the graph of the movement!

Using the motion graph we can find more information about how a mobile moves:

The graph of rectilinear and uniform motion is a straight line.
If the mobile is at rest, the motion graph is a horizontal line.
To draw the graph of the motion it is enough to represent at least two points that together, will determine the right of the graph.
The straight line representing the rectilinear and uniform motion is more inclined (forming a larger angle with the horizontal) when the speed is higher.

🔓 Solved problems

2. The graph of the movement of a mobile is represented in the following figure:

a) What are the positions of the mobile at the moments: t₁ = 0 h, respectively t₂ = 2 h?

b) Is the mobile moving away or closer to the landmark?

c) When does the mobile reach the 120 km position?

d) When does the mobile reach the landmark?

e) What is the speed of the mobile in m / s?

Solution:

a) At t₁ = 0 h, the mobile is in position x₁ = 200 km. From origin, we climb vertically (position axis) until we intersect the graph and thus determine the position x₁ = 200 km. At t₂ = 2 h, the mobile is in position x₂ = 100 km. We climb vertically (position axis) until we intersect the graph and from the graph we go horizontally dotted, until we intersect the position axis, so we determine the position x₂ = 100 km.

b) The mobile is approaching the landmark (position 0 km), because the positions of the mobile decrease with increasing time.

c) At 120 km, the mobile is 1.5 hours after departure. We start with a dotted line of 120 km horizontally, until we meet the graph and from here, we descend dotted vertically on the time axis.

d) In the landmark, position 0 km, we have a time of 4 h. Originally, we go horizontally (time axis) until we intersect the graph and thus determine the time of 4 h.

e) We write the speed formula: