newtonian mechanics - What is wrong with the energy of a particle, of which the mass increase with time?

Let a particle move in space with constant velocity $v$. Its mass is directly proportional to time: $m=\mu t$, where $\mu$ is a constant with dimension kg $\text{s}^{-1}$. A single force acts on the particle so that it can maintain its constant velocity $v$. No other forces act on the particle.

This is not strange at all: just imagine you are pushing a trolley, and people around you continuously throw stationary things into the trolley. That's how it gains mass.

Now here is the problem:

The particle has no potential energy. Let $E$ denote the total energy inside the system, then $E$ is also the total kinetic energy. On one hand, we have

$$ dE=d(\frac{1}{2}mv^2)=d(\frac{1}{2}\mu v^2t)=\frac{1}{2}\mu v^2dt. $$

On the other hand, we have $$ dE=Fdx=\frac{dp}{dt}dx=vdp=vd(\mu t v)=\mu v^2dt, $$ which differs for the first expression by a factor of $2$. What's wrong? Why energy disappears?