Answer
The object travels 7.78 meters in the first 5.00 seconds.
Work Step by Step
$F(t) = (16.8~N/s)~t$
$a(t) = \frac{F(t)}{m} = \frac{(16.8~N/s)~t}{45.0~kg}$
$a(t) = (0.3733~m/s^3)~t$
We can use $a(t)$ to find $v(t)$.
$v(t) = v_0 + \int_{0}^{t}a(t)~dt$
$v(t) = 0 + \int_{0}^{t}(0.3733~m/s^3)~t~dt$
$v(t) = (0.1867~m/s^3)~t^2$
We can use $v(t)$ to find $x(t)$.
$x(t) = x_0 + \int_{0}^{t}v(t)~dt$
$x(t) = 0 + \int_{0}^{t}(0.1867~m/s^3)~t^2~dt$
$x(t) = (0.06223~m/s^3)~t^3$
At t = 5.00 s:
$x = (0.06223~m/s^3)(5.00~s)^3$
$x = 7.78~m$
The object travels 7.78 meters in the first 5.00 seconds.
