Final answer:
To simplify the expression, we first calculate the square of each velocity and then multiply by the mass for each term. After performing the calculations, we find that the simplified expression is -9564 kg·m²/s², which pertains to a combined kinetic energy calculation.
Step-by-step explanation:
To simplify the expression 4kg•(3m/s)²-6kg•(40m/s)², we need to apply basic arithmetic operations on the terms given. First, we calculate the squares of the velocities and then multiply them by their respective mass. After doing the calculations, we subtract the second term from the first. So, let's perform the operations:
- Calculate the square of 3 m/s: (3 m/s)² = 9 m²/s².
- Multiply the result by 4 kg: 4 kg • 9 m²/s² = 36 kg·m²/s².
- Calculate the square of 40 m/s: (40 m/s)² = 1600 m²/s².
- Multiply the result by 6 kg: 6 kg • 1600 m²/s² = 9600 kg·m²/s².
- Now subtract the second term from the first: 36 kg·m²/s² - 9600 kg·m²/s² = -9564 kg·m²/s².
The simplified expression is -9564 kg·m²/s², which represents the combined kinetic energy, given the mass and velocity squared.