Question

How fast is a 30 kg child runnning if her kinetic energy is 500 J?

Answer 1

`\displaystyle v = 5.7735 \ m/s`

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

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:
`\displaystyle KE = (1)/(2) mv^2`

• KE is Kinetic Energy (in J)
• m is mass (in kg)
• v is velocity (in m/s)

Step-by-step explanation:

Step 1: Define

Mass m = 30 kg

Kinetic Energy KE = 500 J

Step 2: Solve for v

1. Substitute [KEF]:
   `\displaystyle 500 = (1)/(2)(30)v^2`
2. Multiply:
   `\displaystyle 500 = 15v^2`
3. Isolate v term:
   `\displaystyle (100)/(3) = v^2`
4. Isolate v:
   `\displaystyle (10√(3) )/(3) = v`
5. Rewrite:
   `\displaystyle v = (10√(3) )/(3) \ m/s`
6. Evaluate:
   `\displaystyle v = 5.7735 \ m/s`