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If I drop a pinewood derby car from 4 feet I know it hits the ground in half a second at about 10.6 mph. If it rolls down the track (starting at 4 feet) it takes longer, but is it possible for it to travel faster than 10.6 mph at any point?

I believe it will not travel faster but I can't prove it to myself.

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    $\begingroup$ Think about energy $\endgroup$
    – fqq
    Feb 12, 2016 at 20:01
  • $\begingroup$ More specifically, what type of energy does it have before you drop it and what type does it have at the bottom? Where can energy come from to speed it up? $\endgroup$
    – pentane
    Feb 12, 2016 at 20:25

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You have to approach this from an energy standpoint. You start with a certain amount of energy, in this case gravitational potential energy, which is dependent on the initial height ($h=4\ \text{ft}$). At the end, you have a final energy, in the form of kinetic energy, which is given by $\frac{1}{2}mv^2$. With no other energy terms involved (meaning you don't push it, or there is no drag or friction to drain energy), the final velocity will be the same no matter how the car gets down to the final height of 0. Other drag terms will only reduce the energy that the car has, which will reduces the final speed. The maximum velocity for the car can be solved for by using conservation of energy:

$$mgh = \frac{1}{2}mv_{max}^2$$ $$v_{max} = \sqrt{2gh}$$

which you can see is only dependent on the initial height, $h$.

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  • $\begingroup$ I understand. To go faster than 10.6 mph would mean the car would have more kinetic energy than simply dropping it. which isn't possible because there would be more energy lost to friction. Thanks $\endgroup$
    – Eye Kneel
    Feb 12, 2016 at 21:16
  • $\begingroup$ Yes, and more specifically, it would have to have another source of energy to go faster, which it does not in this case. $\endgroup$
    – tmwilson26
    Feb 12, 2016 at 21:47

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