A cart loaded with sand moves along a horizontal floor due to a constant force `F` coinciding in direction with cart's velocity vector. In the process, the sand spills through a hole in the bottom with a constant rate `mukg//s.` Find the acceleration and velocity of the cart at the moment `t`, if at the initial moment `t=0` the cart with loaded sand had mass `m_(0)` and its velocity was equal to zero. Friction is to be neglected.
Text Solution
AI Generated Solution
To solve the problem, we will follow these steps:
### Step 1: Understand the system
We have a cart with an initial mass \( m_0 \) that is moving due to a constant force \( F \). The cart is losing mass at a constant rate \( \mu \) kg/s due to sand spilling out of a hole in the bottom. Initially, at \( t = 0 \), the velocity \( v = 0 \).
### Step 2: Express the mass of the cart at time \( t \)
The mass of the cart at any time \( t \) can be expressed as:
\[
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CENGAGE PHYSICS ENGLISH-CENTRE OF MASS-INTEGER_TYPE
