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Recall the formula for kinetic energy.

Physics

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Answer

The car\text{The car}

Step-by-step solution

4 steps
  1. Recall the formula for kinetic energy.

    The kinetic energy (K.E.) of an object is given by the formula:

    K.E.=12mv2K.E. = \frac{1}{2} m v^2

    where mm is the mass and vv is the speed.

  2. Rearrange the formula to solve for speed squared (v2v^2).

    Multiply both sides by 2:

    2K.E.=mv22 K.E. = m v^2

    Divide both sides by mm:

    v2=2K.E.mv^2 = \frac{2 K.E.}{m}
  3. Analyze the relationship between speed and mass.

    The problem states that the car and the truck have the same kinetic energy. This means K.E. is constant for both vehicles. Also, 2 is a constant.
    Therefore, we can see that v2v^2 is inversely proportional to mm:

    v2∝1mv^2 \propto \frac{1}{m}

    This implies that if the mass (mm) is smaller, the speed squared (v2v^2) must be larger to maintain the same kinetic energy. Consequently, the speed (vv) will also be larger.

  4. Apply the relationship to the car and truck.

    We are given that the truck has more mass than the car.
    Since v2∝1mv^2 \propto \frac{1}{m}, the object with less mass will have a greater speed.
    The car has less mass than the truck.

    Therefore, the car has greater speed.

    The car has greater speed.

    The car\text{The car}
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