An Illustration from Dynamics: Velocity, Acceleration, etc

Excerpts

• An Illustration from Dynamics: Velocity, Acceleration, etc

  The number of units of length described in a unit of time is called the *velocity*; thus

• An Illustration from Dynamics: Velocity, Acceleration, etc

  Suppose a point moving along a straight line uniformly; that is, if the whole length described be divided into any number of equal parts, however great, each of those parts is described in the same time.

• An Illustration from Dynamics: Velocity, Acceleration, etc

  we can, at the end of every time, assign a uniform velocity, which shall represent, more nearly than any other, the rate at which the point is moving.

• An Illustration from Dynamics: Velocity, Acceleration, etc

  And since, when $x$ is the space described, $\phi' t$ is the limit of $\dfrac{dx}{dt}$, the velocity is also this limit; that is, when a point does not move uniformly, the velocity is not represented by any increment of length divided by its increment of time, but by the limit to which that ratio continually tends, as the increment of time is diminished.

• An Illustration from Dynamics: Velocity, Acceleration, etc

  That is, at the end of four seconds a falling body moves at the rate of $128\frac{2}{3}$ feet per second.

Equations

• An Illustration from Dynamics: Velocity, Acceleration, etc

  a = 16\frac{1}{12}

  The constant a in the falling-body law (distance = a t^2, with time in seconds and distance in feet) is taken as 16 1/12, very nearly.

Problems

No exercises in this chapter.