Q5.4 Kinetic energy and linear momentum (S)

How fast must you walk or run to have

  1. the same kinetic energy
  2. the same momentum

as a 1600 kg car moving at 1 kmh-1.

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Hint

Straightforward if you remember the definitions of linear momentum (Key Point 4.5)and kinetic energy (Key Point 3.8)
 

Solution

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Solution

Let’s denote my mass and (magnitude of) velocity by m and v respectively, and that of the car by mc and vc.
  1. Equal kinetic energy:

    \[ \frac{1}{2} m v^2 = \frac{1}{2} m_c v_c^2 \]
    Therefore
    \[ v = \sqrt{\frac{m_c}{m}} v_c \]

    If we assume your mass to be 75 kg, then you would have to run at 4.61 kmh-1

  2. Equal momenta:
    mv=mvc
    therefore v=vcmc/m. Again taking m=75 kg, I have to run at 21.33 kmh-1, which is about equivalent to a five minute mile pace.