## University Physics with Modern Physics (14th Edition)

$x(t) = \alpha t^2 - \beta t^3$ $\alpha = 1.50~m/s^2$ $\beta = 0.0500~m/s^3$ (a) At t = 0, $x = (1.50~m/s^2)(0)^2 - (0.0500~m/s^3)(0)^3 = 0$ At t = 2.00 s, $x = (1.50~m/s^2)(2.00~s)^2 - (0.0500~m/s^3)(2.00~s)^3$ $x = 5.60~m$ $average~velocity = \frac{\Delta x}{\Delta t} = \frac{5.60~m- 0}{2.00~s} = 2.80~m/s$ (b) At t = 0, $x = (1.50~m/s^2)(0)^2 - (0.0500~m/s^3)(0)^3 = 0$ At t = 4.00 s, $x = (1.50~m/s^2)(4.00~s)^2 - (0.0500~m/s^3)(4.00~s)^3$ $x = 20.8~m$ $average~velocity = \frac{\Delta x}{\Delta t} = \frac{20.8~m- 0}{4.00~s} = 5.20~m/s$ (c) At t = 2.00 s, $x = (1.50~m/s^2)(2.00~s)^2 - (0.0500~m/s^3)(2.00~s)^3$ $x = 5.60~m$ At t = 4.00 s, $x = (1.50~m/s^2)(4.00~s)^2 - (0.0500~m/s^3)(4.00~s)^3$ $x = 20.8~m$ $average~velocity = \frac{\Delta x}{\Delta t} = \frac{20.8~m- 5.60~m}{2.00~s} = 7.60~m/s$