Classical Mechanics and Newtonian Dynamics Practice Questions | GRE Subject Test Physics

Classical Mechanics and Newtonian Dynamics

Question 1 of 30

Time left: 00:00

A rocket moves in deep space (ignore gravity). It ejects fuel at constant speed \(u\) relative to the rocket. At \(t=0\), the rocket has mass \(m_0\) and speed \(v_0\) in an inertial frame. Fuel is expelled at a constant rate \(\dot m=-k\) (so \(m(t)=m_0-kt\)). What is the rocket speed \(v(t)\) for \(0\le t< m_0/k\)?

Select one option.

\(v(t)=v_0+u\ln\!\left(\dfrac{m_0}{m_0-kt}\right)\)
\(v(t)=v_0+u\left(\dfrac{m_0}{m_0-kt}\right)\)
\(v(t)=v_0+u\left(\dfrac{m_0-kt}{m_0}\right)\)
\(v(t)=v_0+\dfrac{u\,kt}{m_0}\)
\(v(t)=v_0+u\ln\!\left(\dfrac{m_0-kt}{m_0}\right)\)

You have used 0 of 1 attempt

Next ▶