For projectile motion, for example if i set my coordinate system as positive so that means that the acceleration and the max height (dy) is going to be positive?
Here's how you can think about this.
Now, let's say that you launch a projectile straight up and that it reaches a maximum height of 100 meters.
You can break down its movement into two parts
- moving up towards maximum height
- falling from maximum height
If you take the upward direction to be positive and the ground level to be sero, then the displacement of the projectile will be
- positive on its way up, since it goes from ground level to 100m in the assigned positive direction;
- negative on its way down, since now it is moving from 100m to ground level;
What about the gravitational acceleration? You know that gravity is always pulling objects towards the ground. If the upward direction remains the positive direction, then
- negative while the projectile moves towards maximum height, i.e. as it climbs, since
#g#is a vector directed towards the surface of the Earth and the projectile is moving in the opposite direction;
- positive while the projectile is falling from maximum height, since now the direction of gravity is the same as the direction of the projectile.
So, in this example, if you take
- on the projectile's way up
#+"100 m" = v_0 * t + 1/2 * (-g) * t^2#
Positive displacement and negative gravitational acceleration.
- on the projectile's way down
Negative displacement and positive gravitational acceleration.