2010013701

The motion of two bodies is given by equations $$s_1=\frac{1}{2}{t}^2+6t+1\text{,}{s}_2=\frac{1}{3}{t}^3+t^2+4,$$ where the positions $s_1$ and $s_2$ are given in meters and the time $t$ in seconds. Determine at what time both bodies will move at the same speed. $$$$ Hint: Instantaneous velocity can be expressed as the derivative of a position function $s(t)$ with respect to time: $v(t)=\frac{\mathrm{d}s}{\mathrm{d}t}$.