Answer:
[tex]\displaystyle v = 5.7735 \ m/s[/tex]
General Formulas and Concepts:
Math
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Physics
SI Units
- Speed is m/s (meters per second)
- Energy is J (Joules), equal to 1 N/m (newton per meter)
- Mass is kg (kilograms)
Energy
Kinetic Energy Formula: [tex]\displaystyle KE = \frac{1}{2} mv^2[/tex]
- KE is Kinetic Energy (in J)
- m is mass (in kg)
- v is velocity (in m/s)
Explanation:
Step 1: Define
Mass m = 30 kg
Kinetic Energy KE = 500 J
Step 2: Solve for v
- Substitute [KEF]: [tex]\displaystyle 500 = \frac{1}{2}(30)v^2[/tex]
- Multiply: [tex]\displaystyle 500 = 15v^2[/tex]
- Isolate v term: [tex]\displaystyle \frac{100}{3} = v^2[/tex]
- Isolate v: [tex]\displaystyle \frac{10\sqrt{3} }{3} = v[/tex]
- Rewrite: [tex]\displaystyle v = \frac{10\sqrt{3} }{3} \ m/s[/tex]
- Evaluate: [tex]\displaystyle v = 5.7735 \ m/s[/tex]
