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An automobile with a mass of 1180 kg is traveling at a speed v = [06] ____________________ m/s. a. What is its kinetic energy in SI units? b. What speed (m/s) must an 82.7-kg person move to have the same kinetic energy? c. At what speed (m/s) must a 12.1-g bullet move to have the same kinetic energy? d. What would be the speed (m/s) of the automobile if its kinetic energy were doubled?

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Complete Question:

An automobile with a mass of 1180 kg is traveling at a speed v =2.51 m/s. What is its kinetic energy in SI units? What speed (m/s) must an 82.7-kg person move to have the same kinetic energy? At what speed (m/s) must is 12.1-g bullet move to have the same kinetic energy? What would be the speed (m/s) of the automobile if its kinetic energy were doubled?

Answer:

a) 3717.1 J b) 9.48 m/s c) 783.8 m/s d) 3.55 m/s

Explanation:

a)

  • By definition, the kinetic energy of a mass m with a speed v, is as follows:

      [tex]K = \frac{1}{2} * m *v^{2}[/tex]

  • if m= 1180 Kg, and v= 2.51 m/s, the kinetic energy can be calculated as follows:

       [tex]K = \frac{1}{2} * m *v^{2} = \frac{1}{2} * 1180 kg*(2.51 m/s)^{2} = 3717.1 J[/tex]

b)

  • If the kinetic energy must be the same, and m= 82,7 Kg, we can write the following expression:

       [tex]K = \frac{1}{2} * m *v^{2} = \frac{1}{2} * 82.7 kg*((v)(m/s))^{2} = 3717.1 J[/tex]

  • We can solve the above equation as follows:

        [tex]v =\sqrt{\frac{2*K}{m} } = \sqrt{\frac{2*3717.1J}{82.7kg} } = 9.48 m/s[/tex]

c)

  • If K remains the same, and m = 12.1 g = 0.0121 kg (in SI units). we can solve for v  as follows:

       [tex]v =\sqrt{\frac{2*K}{m} } = \sqrt{\frac{2*3717.1J}{0.0121kg} } = 783.8 m/s[/tex]

d)

  • Now, if the kinetic energy were doubled, we would have the following equation:

       [tex]K = \frac{1}{2} * m *v^{2} = \frac{1}{2} * 1180 kg*((v) m/s)^{2} = 3717.1 J * 2 = 7434.2 J[/tex]

  • We can solve for the new speed v as follows:

        [tex]v =\sqrt{\frac{2*K}{m} } = \sqrt{\frac{2*7434.2J}{1180kg} } = 3.55 m/s[/tex]

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