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At what speed does a 2000 kg compact car have the same kinetic energy as a 18000 kg truck going 21 km/hr?

Respuesta :

cjrodriguez89

Answer:

v = 17.5 m/s = 63 km/h

Explanation:

  • The general expression for the kinetic energy of one moving object is as follows:

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

       where m = mass of the object, v= speed of the object.

  • In order to get the value of the kinetic energy of the truck in Joules, we need to convert km/hr to m/s first, as follows:

       [tex]21 km/hr * \frac{1 hr}{3600s}*\frac{1000m}{1 km} = 5.83 m/seg (2)[/tex]

  • Now, replacing (2) and m = 18000 kg in (1), we get:

       [tex]K = \frac{1}{2}*18000 kg *(5.83m/s)^{2} = 306250 J (3)[/tex]

  • This value must be the same for the 2000 kg compact car, so we can write:

       [tex]K = 306250 J = \frac{1}{2}*2000 kg *v^{2} (4)[/tex]

  • Solving for v, we get:

       [tex]v = \sqrt{\frac{306250}{1000} (m/s)2} = 17. 5 m/s = 63 km/h (5)[/tex]

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