Why must vertical acceleration always be negative on projectile motion?

[hamsterpower7]

$$y= y_0 + v_(y0)t - 1/2gt^2$$

why is it -1/2 gt^2?
what if somebody was to throw ball downward?
is that still negative velocity?


wait, does negative in velocity mean direction?? or slowing down
kind of confused while writing this question
if it is direction why is it negative for throwing the ball upward?

 

[bp_psy]

$$y= y_0 + v_(y0)t - 1/2gt^2$$

why is it -1/2 gt^2?
what if somebody was to throw ball downward?
is that still negative velocity?wait, does negative in velocity mean direction?? or slowing down
kind of confused while writing this question
if it is direction why is it negative for throwing the ball upward?

The signs are only due to your choice in coordinates. You can chose different coordinates and make your acceleration positive.The ones you use now are just the least awkward for this situation.Try to flip or rotate your coordinates and get the equations describing parabolic motion. The physics is the same the equations are not.

 

[Pengwuino]

As bp_psy stated, it is a matter of what your coordinate system convention is.

If you decide "up" is positive, then the acceleration is always negative (since it points down towards what is typically the Earth in these projectile motion problems). If the projectile is moving upwards, the velocity is positive; if it is moving downwards, the velocity is negative. If you decide "up" is negative, the acceleration is always positive because it points down and will have opposite sign. If the projectile is moving up, the velocity is negative; if it is moving downward, the velocity is positive.

The idea of "slowing down" and "speeding up" is kind of vague. The positive/negative sign on the velocity or acceleration doesn't tell you if the object is speeding up or slowing down alone. For example, if you throw a ball upwards, the acceleration points downward and at the beginning you could say it is slowing down. However, after it reaches the top, comes to rest, and begins falling again, you could then say it's speeding up! What "speeding up/slowing down" really refers to is the magnitude of the velocity (in other words, what the velocity is regardless of the sign).

 

[sophiecentaur]

You can use any sign you like but you need to be consistent, once you have made the choice. Slowing down on the way up is the same (-g) as speeding up as you are dropping downwards because the sign for direction is different for up and down.
You just need to let the Maths do the work for you and interpret the answer that comes out of the other end correctly. It can't let you down.

 

[PJC01]

I can explain the concept of vertical acceleration and its relation to projectile motion. The equation you have mentioned, y= y_0 + v_(y0)t - 1/2gt^2, is known as the kinematic equation for position in the y-direction. The -1/2gt^2 term represents the effect of gravity on the vertical motion of a projectile.

In projectile motion, an object is launched into the air at an angle and follows a curved path due to the combined effects of its initial velocity and gravity. The acceleration due to gravity, denoted by g, is always acting in the downward direction. This means that no matter which direction the projectile is moving in, the acceleration due to gravity will always act in the opposite direction, i.e. downwards.

Now, to answer your question, yes, negative in velocity does refer to the direction of motion. In this equation, the negative sign indicates that the acceleration due to gravity is acting in the opposite direction to the initial velocity. This is true for both upward and downward motion.

When an object is thrown downward, its initial velocity is in the downward direction, and the acceleration due to gravity is also acting downwards. This means that the object is accelerating in the same direction as its initial velocity, resulting in a positive acceleration. However, since the equation is written in terms of displacement, the acceleration term is written as -1/2gt^2 to account for the change in direction.

In summary, the -1/2gt^2 term in the kinematic equation for position in the y-direction represents the effect of gravity on the vertical motion of a projectile. It is always negative because gravity acts in the opposite direction to the initial velocity of the object. This is true for both upward and downward motion. I hope this helps clarify any confusion you may have had.