135. The velocity of a point moving in a straight line is given by the equation $v=t^{2}-8 t+3$. Find the equation of motion of the point.
Solution. $1^{0}$. It is known that the velocity of a body in rectilinear motion is the derivative of the path $s$ with respect to time $t$, i.e., $v=\frac{d s}{d t}$, from which we have $d s=$ $=v d t$. Then we have $d s=\left(t^{2}-8 t+3\right) d t$.

$2^{0}$. To find the equation of motion, we integrate both sides of the obtained equality:

$$
\int d s=\int\left(t^{2}-8 t+3\right) d t ; \quad s=\frac{1}{3} t^{3}-4 t^{2}+3 t+C
$$

This is the desired equation.

In the following problems of this section, rectilinear motion is considered.