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