Rectilinear Motion Problems And Solutions Mathalino -

Use ( a = v \fracdvds = -0.5v ). Cancel ( v ) (assuming ( v \neq 0 )):

[ \int dv = \int 6t , dt ] [ v = 3t^2 + C_1 ] rectilinear motion problems and solutions mathalino

Topics: 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

From ( v = \fracdsdt = 20 - 0.5s ). Separate variables: In engineering mechanics, this is the simplest form

[ \fracdvv = -0.5 , dt ] Integrate: [ \ln v = -0.5t + C ] At ( t=0, v=20 \Rightarrow \ln 20 = C ). [ \ln\left( \fracv20 \right) = -0.5t ] [ \boxedv(t) = 20e^-0.5t ]

Ground: ( s = 0 ). Use ( v^2 = v_0^2 + 2a(s - s_0) ): [ v^2 = 20^2 + 2(-9.81)(0 - 50) ] [ v^2 = 400 + 981 = 1381 ] [ v = -\sqrt1381 \quad (\textnegative because downward) ] [ \boxedv \approx -37.16 , \textm/s ]

[ \int ds = \int 3t^2 , dt ] [ s = t^3 + C_2 ]