Alright, let's break down what we understand by the given accelerations:
### Acceleration of [tex]\( +2 \, \text{m/s}^2 \)[/tex]
1. Definition: Acceleration describes how quickly an object's velocity is changing over time.
2. Positive Sign: The plus sign (+) indicates that the acceleration is in the same direction as the velocity. This means the object is speeding up.
3. Unit Breakdown:
- [tex]\( \text{m} \)[/tex] stands for meters, which is a unit of distance.
- [tex]\( \text{s} \)[/tex] stands for seconds, which is a unit of time.
- [tex]\( \text{m/s}^2 \)[/tex] means meters per second squared, which is a unit of acceleration.
4. Explanation: An acceleration of [tex]\( +2 \, \text{m/s}^2 \)[/tex] means that for every second that passes, the velocity of the object increases by 2 meters per second.
Interpretation: Therefore, the velocity of the object is increasing by 2 meters per second every second.
### Acceleration of [tex]\( -2 \, \text{m/s}^2 \)[/tex]
1. Definition: Similarly, acceleration describes the rate of change of velocity.
2. Negative Sign: The minus sign (-) indicates that the acceleration is in the opposite direction to the velocity. This means the object is slowing down or decelerating.
3. Unit Breakdown:
- [tex]\( \text{m} \)[/tex] stands for meters.
- [tex]\( \text{s} \)[/tex] stands for seconds.
- [tex]\( \text{m/s}^2 \)[/tex] means meters per second squared.
4. Explanation: An acceleration of [tex]\( -2 \, \text{m/s}^2 \)[/tex] means that for every second that passes, the velocity of the object decreases by 2 meters per second.
Interpretation: Therefore, the velocity of the object is decreasing by 2 meters per second every second.
In summary:
- An acceleration of [tex]\( +2 \, \text{m/s}^2 \)[/tex] indicates that the object's velocity is increasing at a rate of 2 meters per second every second.
- An acceleration of [tex]\( -2 \, \text{m/s}^2 \)[/tex] indicates that the object's velocity is decreasing at a rate of 2 meters per second every second.
