Chapter 12 - Kinematics of a Particle - Section 12.3 - Rectilinear Kinematics: Erratic Motion - Problems - Page 28: 36

$$ \begin{aligned} & s=0.4 t^2 \\ & v=\frac{d s}{d t}=0.8 t \\ & a=\frac{d v}{d t}=0.8 \\ & s=24(t-30)+360 \\ & v=\frac{d s}{d t}=24 \\ & a=\frac{d v}{d t}=0 \end{aligned} $$

$$ \begin{aligned} & 0 \leq t \leq 30: \\ & s=0.4 t^2 \\ & v=\frac{d s}{d t}=0.8 t \\ & a=\frac{d v}{d t}=0.8 \\ & 30 \leq t \leq 40: \\ & s-360=\left(\frac{600-360}{40-30}\right)(t-30) \\ & s=24(t-30)+360 \\ & v=\frac{d s}{d t}=24 \\ & a=\frac{d v}{d t}=0 \end{aligned} $$