Question

A frieght car of mass m starts moving to the right due to constant horizontal force F. Sand spills on the car on a stationary hooper. The velocity of loading is constant equal to X km/sec. Find the time dependence of the velocity and the acceleration of the car in process of loading

Answer 1

Answer on Question #79714 - Physics - Mechanics | Relativity

A freight car of mass $m$ starts moving to the right due to constant horizontal force $F$. Sand spills on the car on a stationary hooper. The velocity of loading is constant equal to $X \, \text{km/sec}$. Find the time dependence of the velocity and the acceleration of the car in process of loading

$$F = m \cdot a;$$ $$a = F / m = F / (m_0 + X \cdot t)$$ $$v = \int_0^t a \, dt = \int_0^t \frac{F}{m_0 + X \cdot t} \, dt = \frac{F}{X} \ln \frac{m_0 + X \cdot t}{m_0}$$

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