Heat released before the speed halves

A 0.50 kg conductor moves horizontally at 3.0 m/s into a regime modeled by a magnetic braking force F = −cv with c = 0.25 kg/s. No driving force acts. The lost kinetic energy is converted into heat in the conductor.

How much heat has been released when the speed first reaches 1.5 m/s?

Organize the givens & assumptions

Mass: 0.50 kg
Initial speed: 3.0 m/s
Final speed: 1.5 m/s
Linear braking coefficient: 0.25 kg/s

The stated effective braking model applies throughout; ignore other losses and any change of stored field energy between the compared states. The conductor is the heat-receiving part of this model.

A $1.125\ \mathrm J$
B $1.6875\ \mathrm J$
C $2.25\ \mathrm J$
D $0.5625\ \mathrm J$

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