Solved problem: Position Equation of the S.H.S. Madrid-Barcelona (Spain High Speed train)

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Statement

difficulty

The S.H.S. Madrid-Barcelona during the first stage of its trip travels east at a rate of 50 m each second and North at 30 m each second. Calculate:

The motion x-coordinate as function of time
The motion y-coordinate as a function of time
The position equation of the train for the studied stretch
The distance to the origin of the section as a function of time

Solution

$x (t) = 50 t$ m
$y (t) = 30 t$ m
$\vec{r} (t) = 50 t \vec{i} + 30 t \vec{j}$
$r (t) = \sqrt{(50 t)^{2} + (30 t)^{2}} = 58.3 t$ m

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

|\vec{r}| = \sqrt{x^{2} + y^{2}}

Position Vector

\vec{r} (t) = x (t) \vec{i} + y (t) \vec{j}

Trajectory and Equation of Position

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Position Equation of the S.H.S. Madrid-Barcelona (Spain High Speed train)

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Solution

Formulas worksheet