A cart loaded with sand moves along horizontal floor due to a constant force F, coinciding in direction with the velocity of cart. In the process, the sand spills through a hole in the bottom with a constant rate 𝜇 kg/s. If at the initial moment t = 0, the cart with loaded sand had the mass m0 and its velocity was equal to zero (neglect friction). Then,

Q: A cart loaded with sand moves along horizontal floor due to a constant force F, coinciding in direction with the velocity of cart. In the process, the sand spills through a hole in the bottom with a constant rate 𝜇 kg/s. If at the initial moment t = 0, the cart with loaded sand had the mass m0 and its velocity was equal to zero (neglect friction). Then,

(a) the acceleration of the cart at time t is $\frac{F}{m_0 -\mu t}$

(b) the velocity of the cart at time t is $\frac{F}{\mu} ln (\frac{m_0}{m_0 – \mu t})$

(c) the acceleration of the cart at time t is $\frac{F}{(m_0 + μt)} $

(d) the velocity of the cart at time t is $\frac{F}{2 \mu} ln (\frac{m_0}{m_0 – \mu t})$

Ans: (a) , (b)