2024-241

Consider a particle moving in a one dimensional space. Its acceleration is proportional to the square of its velocity. Also, at $t=0$, it has a velocity 2 m/s and at $t=1$, it runs at 1 m/s. Consider that the particle starts at $x=0$ m.

With that in mind, choose the alternative that correctly describes the particle's position, $x(t)$, with respect to time.

1. $x(t)=(\ln (1+t))/2$
2. $x(t)=1+\ln (2+t^2)$
3. $x(t)=2+\ln (1+t^2)$
4. $x(t)=2\ln (1+t)$
5. None of the above.

Original idea by: Vitor Antônio Pimenta Silva