Listing DetailsTopics: Dynamics, Engineering Mechanics, Calculus-Based Kinematics What is Rectilinear Motion? Rectilinear motion refers to the movement of a particle along a straight line. In engineering mechanics, this is the simplest form of motion. The position of the particle is described by its coordinate ( s ) (often measured in meters or feet) along the line from a fixed origin.
Use ( a = v \fracdvds = -0.5v ). Cancel ( v ) (assuming ( v \neq 0 )): rectilinear motion problems and solutions mathalino
[ \int dv = \int 6t , dt ] [ v = 3t^2 + C_1 ] The position of the particle is described by
[ \int ds = \int 3t^2 , dt ] [ s = t^3 + C_2 ] Integrate:
[ v , dv = 4s , ds ] Integrate: [ \fracv^22 = 2s^2 + C ] At ( s = 1 ) m, ( v = 0 ): [ 0 = 2(1)^2 + C \quad \Rightarrow \quad C = -2 ] Thus: [ \fracv^22 = 2s^2 - 2 ] [ v^2 = 4s^2 - 4 ] [ \boxedv(s) = \pm 2\sqrts^2 - 1 ]
We know ( v = \fracdsdt = 3t^2 ). Integrate: