To find the energy equivalent of an object with a mass of 2.5 kg, we use Albert Einstein's famous equation from the theory of relativity:
[tex]\[E = mc^2\][/tex]
Where:
- [tex]\(E\)[/tex] is the energy,
- [tex]\(m\)[/tex] is the mass of the object (in kilograms),
- [tex]\(c\)[/tex] is the speed of light in a vacuum (approximately [tex]\(3.0 \times 10^8\)[/tex] meters per second).
Given:
- [tex]\(m = 2.5\)[/tex] kg,
- [tex]\(c = 3.0 \times 10^8\)[/tex] m/s.
Let's compute the energy step-by-step.
1. Write down the formula:
[tex]\[ E = mc^2 \][/tex]
2. Substitute the given values:
[tex]\[ E = 2.5 \times \left(3.0 \times 10^8\right)^2 \][/tex]
3. Calculate [tex]\( \left(3.0 \times 10^8\right)^2 \)[/tex]:
[tex]\[ \left(3.0 \times 10^8\right)^2 = 9.0 \times 10^{16} \][/tex]
4. Now, multiply this result by the mass:
[tex]\[ E = 2.5 \times 9.0 \times 10^{16} \][/tex]
5. Simplify the multiplication:
[tex]\[ E = 22.5 \times 10^{16} \][/tex]
6. Express the result in proper scientific notation:
[tex]\[ E = 2.25 \times 10^{17} \][/tex]
Therefore, the energy equivalent of an object with a mass of 2.5 kg is:
[tex]\[ 2.25 \times 10^{17} \][/tex]
So, the correct answer from the given options is:
[tex]\[ \boxed{2.25 \times 10^{17}} \][/tex]
