a = -g because it defines the direction of gravitational acceleration relative to a chosen coordinate system. Here's a breakdown:
The question refers to a situation where 'a' represents acceleration and 'g' represents the acceleration due to gravity. The minus sign indicates the direction of gravitational acceleration.
-
Gravitational Acceleration: Gravity always pulls objects towards the center of the Earth.
-
Coordinate System: We define a coordinate system to describe motion. Often, we define upwards as the positive direction and downwards as the negative direction.
-
Therefore: If we define upwards as positive, then the acceleration due to gravity, which acts downwards, must be negative. Hence,
a = -g. As stated in the reference, "At all points on the trajectory of a projectile, the gravitational acceleration points in the same direction, which is downwards toward the center of the Earth. So, the sign for the gravitational acceleration is always negative." This is towards the center of the Earth.
Example:
Imagine throwing a ball upwards.
- You define up as the positive direction.
- Gravity is pulling the ball downwards.
- Therefore, the ball's acceleration due to gravity is negative,
a = -g.
| Variable | Description | Direction (Up as Positive) |
|---|---|---|
a |
Acceleration of the object | Downward |
g |
Magnitude of gravitational acceleration | Always Positive |
-g |
Gravitational acceleration | Downward |
The magnitude of g is approximately 9.8 m/s2. The negative sign in front of g only indicates the direction of the acceleration in relation to the coordinate system used to solve a given problem.
