Final answer:
The mass of the motorcycle can be calculated using the work-kinetic energy theorem. The work done on the motorcycle is the difference in its kinetic energy before and after work is applied. The closest calculated mass of the motorcycle, considering the examined physics principles, is approximately 606.06 kg, which most closely approximates answer choice A) 625 kg.
Step-by-step explanation:
The question involves the conservation of energy and the work-energy principle in physics. To find the mass of the motorcycle, we can use the work-kinetic energy theorem which states that the work done on an object is equal to the change in its kinetic energy. The kinetic energy (KE) can be calculated using the equation KE = \( \frac{1}{2}mv^{2} \), where m is the mass and v is the velocity of the motorcycle.
Let's first calculate the initial kinetic energy using the initial velocity (v1 = 4 m/s) and the final kinetic energy using the final velocity (v2 = 7 m/s). The work done on the motorcycle (W = 10,000 J) is the difference between the final and initial kinetic energies (KE2 - KE1).
Initial KE:\( KE1 = \frac{1}{2}m(4)^{2} = 8m \) J
Final KE:\( KE2 = \frac{1}{2}m(7)^{2} = 24.5m \) J
Since work done on the motorcycle is the change in kinetic energy:
\( W = KE2 - KE1 \)
\( 10000 = ((\frac{1}{2}m(7)^{2}) - (\frac{1}{2}m(4)^{2})) \)
\( 10000 = (24.5m - 8m) \)
\( 10000 = 16.5m \)
\( m = \frac{10000}{16.5} \)
\( m = 606.06 \) kg
This result doesn't match any of the provided options exactly; thus, there might be a typo in the options or an error in the calculations. If you were to round the calculated mass, the closest value would be A) 625 kg.