Never trust that something is true. I think we can easily show that the explanations given above must be appropriate descriptions of reality, without math.
Take a sled of any type, say a skateboard. Place a weight on the skateboard, say a small child, and shove it. Then place more weight on the skateboard and shove it. I think you should be able to understand that the more massive weight is harder to move than the less massive weight. This is a description of inertia
Now, imagine instead of shoving various weights, you drop them. In this case, the only force involved is gravity. We can demonstrate that surface area is what is most important in air resistance rather than weight, as a sail boat that is tacked appropriately moves more quickly than a sail boat with the same weight of sails turned into the wind rather than catching the wind. A good way to negate air resistance without requiring a vacuum is to make similarly sized spheres of different weight. Imagine two similar bowling balls but one has been hollowed out so that it weighs significantly less than the other. Both balls would fall when dropped at the same rate. Alternatively, roll them down a ramp rather than dropping them. Their speed when hitting the bottom would be the same. The acceleration they encounter, which is the change in speed over time, would be the same. You could measure the difference in velocity (velocity is speed in a particular direction) when they hit the ground depending on the height that they were dropped from. If you made repeated experiments, you would notice that velocity at impact is proportional to the time to impact squared. It is repeated observations such as these that led to Newton's description of gravitational interactions.
In the skateboard tests, we showed that it takes more force to move a heavier weight than a lighter weight. In the drop tests, we showed that regardless of weight, similarly shaped objects fall at the same rate. Inertia is the key to why these two seemingly contradictory statements are correct. It makes sense to think that a heavy object will fall faster than a light object. But, it takes more force to accelerate a heavy object as observed in the skateboard tests. It turns out that after careful measurements, the two things cancel out. The amazing thing is that this was discovered more than three centuries ago.
Edited by JMJones0424, 23 April 2018 - 03:22 AM.