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