Problems And Solutions Mathalino — Rectilinear Motion

We know ( v = \fracdsdt = 3t^2 ). Integrate:

[ v = v_0 + at ] [ s = s_0 + v_0 t + \frac12 a t^2 ] [ v^2 = v_0^2 + 2a(s - s_0) ] rectilinear motion problems and solutions mathalino

Use ( v = v_0 + at ): [ 0 = 20 - 9.81 t \quad \Rightarrow \quad t = \frac209.81 \approx \boxed2.038 , \texts ] We know ( v = \fracdsdt = 3t^2 )

At ( t = 0 ), ( v = 0 \Rightarrow C_1 = 0 ). Thus: [ \boxedv(t) = 3t^2 ] Thus: [ \boxeds(t) = t^3 ] [ \fracdvds = -0

At ( t = 0 ), ( s = 0 \Rightarrow C_2 = 0 ). Thus: [ \boxeds(t) = t^3 ]

[ \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 ]