Chapter 2 - Kinematics in One Dimension - Exercises and Problems - Page 60: 33

(a) $x = 21~m$ (b) $v = 26~m/s$ (c) $a = 24~m/s^2$

(a) $x(t) = 2t^3+2t+1$ At t = 2 s: $x = (2)(2~s)^3+(2)(2~s)+1$ $x = 21~m$ (b) $v(t) = \frac{dx}{dt} = 6t^2+2$ At t = 2 s: $v = (6)(2~s)^2+2$ $v = 26~m/s$ (c) $a(t) = \frac{dv}{dt} = 12t$ At t = 2 s: $a = (12)(2~s)$ $a = 24~m/s^2$