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Solved Problem on Kinematics
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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

Correspondence between S = S0 + vt and S = -10 + 4t

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 S = 0, substituting this value in the given function
\[ 0=-10+4t\\4t=10\\ t=\frac{10}{4} \]
\[ \bbox[#FFCCCC,10px] {t=2.5\;\text{h}} \]

d) For t = 4 h the position will be
\[ S=-10+4.4\\ S=-10+16 \]
\[ \bbox[#FFCCCC,10px] {S=6\;\text{km}} \]
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