When an object falls down why is acceleration of gravity not positive if both acceleration and velocity are both pointing in the same direction toward the earth and speeding up?
Great question! The answer is a matter of perspective.
You’re right, from the ball’s perspective, it is accelerating with a positive value.
However, from the earth’s perspective, the ball is approaching the earth, and therefore the ball’s acceleration is negative.
You can define z as positive up in which case both g and the resulting eventual velocity down are negative.
in this case:
a = -9.81 m/s^2
v = Vi - 9.81 t ,where Vi is initial speed UP
z = initial z + Vi t - 4.9 t^2 [ this is the usual way ]
NOW, if you define z as positive DOWN
a = +9.81
v = Vi + 9.81 t , where Vi is initial speed DOWN
z = initial z + Vi t + 4.9 t^2
Most of us call z positive UP and g down :)
www.bartleby.com/solution-answer/chapter-26-problem-66pq-physics-for-scientists-and-engineers-foundations-and-connections-1st-edition/9781133939146/a-500-nc-charged-particle-is-at-point-b-in-a-uniform-electric-field-with-a-magnitude-of-625-nc/9257f8b6-9734-11e9-8385-02ee952b546e
The acceleration due to gravity is indeed positive, but we perceive it as negative when an object is falling downward. This is because we often assume a positive upward direction, and any acceleration in the downward direction is considered negative.
To understand this, let's break it down step by step:
1. Gravity is a force that pulls objects towards the center of the Earth. It always acts downwards.
2. When an object is falling straight down, its velocity is also directed downwards, towards the Earth's surface.
3. The acceleration due to gravity causes the object's velocity to increase as it falls.
4. According to convention, we consider velocity increasing in the upward direction as positive and velocity decreasing in the upward direction as negative.
5. Therefore, as the object falls down, it is moving in the negative direction (downward), and the velocity is increasing in the negative direction.
6. Since acceleration is the rate of change of velocity, which is negative as the object moves downward, we perceive the acceleration due to gravity as negative.
It's important to note that this is just a convention for the direction of positive and negative in physics. In reality, the acceleration due to gravity is always positive, as it causes objects to speed up downwards.