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

Sagot :

Space

Answer:

[tex]\displaystyle v = 5.7735 \ m/s[/tex]

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: [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

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