Chapter 2 - Kinematics in One Dimension - Exercises and Problems - Page 64: 24

(a) $x = \frac{5}{3}~m$ (b) v = 2 m/s (c) $a = 4~m/s^2$

(a) $v(t) = 2t^2$ $x(t) = x_0+\int_{0}^{t}~v_x(t)~dt$ $x(t) = x_0+\int_{0}^{t}~2t^2~dt$ $x(t) = \frac{2}{3}t^3+1~m$ At t = 1 s: $x = \frac{2}{3}(1~s)^3+1~m$ $x = \frac{5}{3}~m$ (b) $v(t) = 2t^2$ At t = 1 s: $v = (2)(1~s)^2$ $v = 2~m/s$ (c) $a(t) = \frac{dv}{dt}$ $a(t) = 4t$ At t = 1 s: $a = (4)(1~s)$ $a = 4~m/s^2$