Chapter 12 - Kinematics of a Particle - Section 12.7 - Curvilinear Motion: Normal and Tangential Components - Problems - Page 65: 112

$t=1.68$ s

$a_t=1.5s$ $\int_0^s 1.5s ds = \int_{16}^v v dv$ $0.75s^2=0.5v^2-128$ $v=\frac{ds}{dt}=\sqrt{256+1.5s^2}$ $\int_0^s \frac{ds}{\sqrt{s^2+170.7}}=\int_0^t 1.225 dt$ $\ln(s+\sqrt{s^2+170.7})|_0^s=1.225t$ $\ln(s+\sqrt{s^2+170.7})-2.570=1.225t$ At $s=50$ ft, $t=1.68$ s