FYKOS Year 32 Series 3 Problem 5 — pointy · FYKOS 32 #32.3.5

Physics · mechanics

Problem

Consider a point-like particle in one-dimensional space. Initially, the particle is in rest at the origin of coordinates. It can be moved with acceleration from interval

\left (- a , a\right )

. Let

M\left (t\right )

be a set of all possible physical states

\left (x, v\right )

of positions

x

and velocities

v

, which particle can achieve after time

t

is elapsed. If we plot set

M\left (t\right )

into

v(x)

coordinate system we get surface

S\left (t\right )

. Find analytic expression for boundaries of

S\left (t\right )

. Bonus: Find area of

S\left (t\right )

as a funcion of time.}

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