Answer :
Final answer:
To find the energy required to accelerate a 1200-kg car from 3 m/s to 10 m/s, calculate the initial and final kinetic energies and determine the change in kinetic energy. The correct calculation yields an energy requirement of 54.6 kJ, which is not listed in the provided options.
Explanation:
The student is asking to calculate the energy required to accelerate a 1200-kg car from 3 m/s to 10 m/s on a flat road. This can be determined using the work-energy principle which states that the work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy (KEi) and final kinetic energy (KEf) are given by the equations:
- KEi = 1/2 × mass × (initial velocity)2
- KEf = 1/2 × mass × (final velocity)2
By plugging in the values, we get:
- KEi = 1/2 × 1200 kg × (3 m/s)2 = 5400 J
- KEf = 1/2 × 1200 kg × (10 m/s)2 = 60000 J
The energy required (work done) to accelerate the car is the change in kinetic energy (ΔKE), which is KEf - KEi.
ΔKE = 60000 J - 5400 J = 54600 J
Since the question asks for the answer in kilojoules, we convert the energy from joules to kilojoules:
54600 J = 54.6 kJ
However, the provided options do not include 54.6 kJ, so it's possible there may be a typo in the options or an error in the question.
