Answer :
Final answer:
The work done to increase the velocity of a 1500 kg car from 30 km/h to 60 km/h is approximately 156,250 J, using the work-energy principle and the kinetic energy formula.
Explanation:
The amount of work done to increase the velocity of a car from 30 km/h to 60 km/h can be found by using the work-energy principle. This principle states that the work done on an object is equal to the change in its kinetic energy (KE). To calculate the kinetic energy at the two different speeds, we use the formula KE = ½ mv², where m is the mass of the car and v is its velocity.
First, we need to convert the velocities from km/h to m/s:
- 30 km/h = 30 × (1000 m / 3600 s) = 8.333 m/s
- 60 km/h = 60 × (1000 m / 3600 s) = 16.666 m/s
Now, we calculate the initial and final kinetic energies:
- Initial KE = ½ × 1500 kg × (8.333 m/s)²
- Final KE = ½ × 1500 kg × (16.666 m/s)²
Therefore:
- Initial KE = ½ × 1500 kg × 69.444 m²/s² = 52083.5 J
- Final KE = ½ × 1500 kg × 277.778 m²/s² = 208335 J
The work done to increase the velocity is the difference between the final and initial kinetic energies:
Work Done = Final KE - Initial KE = 208335 J - 52083.5 J = 156251.5 J
After rounding to the nearest whole number, the work done is approximately 156,250 J, which corresponds to option A.
