Show me the math. I have no fear of calculus
Already posted, but...
Let's consider the ball in the next frame to have a Mass (m) of 1kg and for this experiment, air resistance is negligible cause it will complicate the math, even though Air Resistance itself is an example of what we are about to do
*.
Our falling object is accelerating due to g. Force is mg
g = 9.8 m/s
2
Our falling object encounters an opposing force that produces an acceleration less than g
F = 5N
since F = ma
a = F/m
a = 5/1
A = 5 m/s
2
To determine the final acceleration we must add the two acceleration vectors. This means that we could get into the laws of co-sines, (c
2=a
2+b
2−2abcosθc
2), but since these to vectors oppose each other we can instead just add their magnitudes and for convention sake we assign all accelerations that oppose the direction of travel as negative, and any in the direction of travel as positive.
So this means that g = +9.8 m/s
2 and A = -5 m/s
2
Thus....
A
Final = g + -A
A
Final = g - A
A
Final = 9.8 - 5
A
Final = 4.8 m/s
2
Our final Acceleration is 4.8 m/s
2 and since it is positive it is in the same direction as our object is travelling (according to our convention above), thus it is still accelerating at 4.8 m/s
2 through the time of the opposing force.
* If the above wasn't enough to convince you, then consider this. Every time something moves on Earth it experiences air resistance (Drag) as a force opposing that motion. If such a force always cause objects to have a negative acceleration when they occurred, then nothing could actually move because as soon as they attempted to accelerate, the air resistance would decelerate them, and their velocity would remain zero.
Rather what we see is that their acceleration is lessened by the air resistance they encounter, hence why we design cars and planes to have as low as possible drag, so they can gain more of their engine's acceleration by having less drag on them meaning that their engine's acceleration minus their drag is maximized and they use less fuel to counter the drag.
Also consider pushing an object across a table. When we do this we create friction, an opposing force. If it decelerated our object then we could not actually push it across the table because as soon as we accelerated our object by pushing it, friction would decelerate it back to velocity of zero. Again it doesn't, it merely lowers the acceleration the object experiences from our pushing.
The only time an object will always experience deceleration when facing a force opposing its direction of travel is when it is moving with a constant velocity because all current forces on that object are balanced. Thus the new force unbalances those forces and creates a negative acceleration.
If an object is already undergoing acceleration due to a force (F
A), then encountering an opposing force (F
O) will do one of three things.
1) if F
O < F
A = Reduced Acceleration
2) if F
O = F
A = No Acceleration
3) if F
O > F
A = Negative Acceleration
