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Solved Problem on Kinematics

The motion of a body is described by the displacement as a function of time

\[
S=-10+4\;t
\]

where the position is measured in kilometers and the time in hours. Find:a) The initial position;

b) The speed;

c) The instant in which the body passes through the origin;

d) The position of the body at time 4 h;

Solution

The function describing the displacement as a function of time is given by

\[ \bbox[#99CCFF,10px]
{S=S_{0}+vt}
\]

with the following associations, we have
a) The initial position of the body

\[ \bbox[#FFCCCC,10px]
{S_{0}=-10\;\text{km}}
\]

b) Speed of the body

\[ \bbox[#FFCCCC,10px]
{v=4\;\text{km/h}}
\]

c) When the body passes the origin of the coordinate system, we have

\[
0=-10+4t\\4t=10\\
t=\frac{10}{4}
\]

\[ \bbox[#FFCCCC,10px]
{t=2.5\;\text{h}}
\]

d) For

\[
S=-10+4.4\\
S=-10+16
\]

\[ \bbox[#FFCCCC,10px]
{S=6\;\text{km}}
\]

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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 .