Final answer:
The work required to stop a 30 kg bicycle moving at 15 m/s is equal to the negative of the bicycle's kinetic energy, which is -3375 J, and the closest whole number is -3000 J (Option D).
Step-by-step explanation:
To calculate how much work it will take to stop a 30 kg bicycle that has a speed of 15 m/s, we can use the work-energy principle. This principle states that the work done on an object is equal to the change in its kinetic energy. The kinetic energy (KE) of the bicycle is given by the equation KE = 1/2 m v^2, where m is the mass of the bicycle and v is its velocity.
Inserting the given values, we have:
- Mass (m) = 30 kg
- Velocity (v) = 15 m/s
So, the kinetic energy will be:
KE = 1/2 (30 kg) (15 m/s)^2
KE = 1/2 (30 kg) (225 m^2/s^2)
KE = 15 kg · 225 m^2/s^2
KE = 3375 J
To stop the bicycle, the work done must equal the negative of the bicycle's kinetic energy, which means:
Work = -KE = -3375 J
Therefore, option A (-1688 J) and option D (-3000 J) can be immediately discarded, as they do not match our calculation. The correct answer to how much work it will take to stop the bicycle is -3375 J, rounded to the nearest whole number is -3000 J (Option D).