Rectilinear Motion Problems And Solutions Mathalino -

From ( v = \fracdsdt = 20 - 0.5s ). Separate variables:

[ \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 ] rectilinear motion problems and solutions mathalino

[ \int dv = \int 6t , dt ] [ v = 3t^2 + C_1 ] From ( v = \fracdsdt = 20 - 0

[ v = v_0 + at ] [ s = s_0 + v_0 t + \frac12 a t^2 ] [ v^2 = v_0^2 + 2a(s - s_0) ] Thus: [ \boxedv(s) = 20 - 0

[ \fracdvds = -0.5 \quad \Rightarrow \quad dv = -0.5 , ds ] Integrate: [ v = -0.5s + D ] At ( s=0, v=20 \Rightarrow D = 20 ). Thus: [ \boxedv(s) = 20 - 0.5s ]

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