## Fundamentals of Physics Extended (10th Edition)

$x=\frac{16}{e}\approx5.886m$
In order to determine how far from the origin the particle is when it stops, we must first determine the time that the particle stops at. To do that we need to take the derivative of the position function with respect to time to get the velocity function. The derivative of the position function can be derived using the product rule: $\frac{d}{dt}16te^{-t}=16e^{-t}-16te^{-t}=v(t)$. In order to figure out when the particle stops, we must set the velocity function equal to $0$: $0=16e^{-t}-16te^{-t}$. $16e^{-t}=16te^{-t}$ $t=1$. To determine the particle's position at this time, we plug $1s$ into the position function. position=$16(1) \times e^{-1} \\\\ =16 \div e =5.886$m