Solved Problem on One-dimensional Motion

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A motorcyclist moves in the opposite direction of an oriented frame of reference, the magnitude of its speed is 40 m/s, and initially, his position is −150 m. Find:

a) The displacement as a function of time;

b) In what time he passes the origin.

Problem data:

- Speed of the motorcyclist: |
*v*| = 40 m/s; - Position at initial time:
*S*_{0}= −150 m.

We choose a reference frame with a positive direction oriented to the right.

Solution

a) We want to find a function of the type

\[
\begin{gather}
\bbox[#99CCFF,10px]
{S=S_0+vt}
\end{gather}
\]

the initial position is given, in the problem
\[
\begin{gather}
\bbox[#FFCCCC,10px]
{S=-150-40t}
\end{gather}
\]

b) When the motorcyclist passes through the origin, we have

\[
\begin{gather}
0=-150\;\mathrm m-\left(40\;\mathrm{\small{\frac{m}{s}}}\right)t\\[5pt]
\left(40\;\mathrm{\small{\frac{m}{s}}}\right)t=-150\;\mathrm m\\[5pt]
t=-\frac{150\;\mathrm{\cancel m}}{40\;\mathrm{\frac{\cancel m}{s}}}\\[5pt]
t=-3.75\;\mathrm{s}
\end{gather}
\]

As there is no negative time, this means that the motorcyclist
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Fisicaexe - Physics Solved Problems by Elcio Brandani Mondadori is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .