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Acceleration is the process by which an object increases its velocity over time. For example, when a car starts from rest, it must accelerate to reach a certain speed. The acceleration is determined by the change in velocity over time and is measured in meters per second squared (\[\text{m/s}^2\]).
In our exercise, the car accelerates at a rate of 2.0 \[\text{m/s}^2\] for 6 seconds. Since the car starts from rest, its initial velocity is zero. Using the formula:\[d = 0.5 \times a \times t^2\]where \(d\) is the distance travelled, \(a\) is the acceleration, and \(t\) is the time. The distance due to acceleration can be calculated by substituting the values into the formula to get 36 meters.
Thus, the car covers a distance of 36 meters during the acceleration phase.

Deceleration is essentially negative acceleration, where an object reduces its speed over time. It is also measured in meters per second squared (\[\text{m/s}^2\]).
In the example exercise, the car initially moves at 12 m/s upon completing its acceleration. It then decelerates at a rate of 1.5 \[\text{m/s}^2\]until it stops for the next sign.
First, we calculate the time needed for this deceleration: \[t = \frac{v}{a}\]. Substituting, we find the time to be 8 seconds. Next, you can calculate the distance during deceleration using:\[d = 0.5 \times a \times t^2\]. Here, the deceleration value is used for \(a\), and you find the distance to be 48 meters. The car covers this distance as it slows down.

Constant velocity means that the object is moving at a steady speed without accelerating or decelerating. Thus, its velocity remains unchanged over the time period considered.
In the context of the exercise, after accelerating for 6 seconds, the car reaches a speed of 12 m/s. It maintains this constant velocity during a 2-second coasting phase. The formula to calculate the distance covered at constant velocity is as simple as:\[d = v \times t\]
This easy calculation leads to a distance of 24 meters covered during the coasting stage. Since there is no acceleration or deceleration during this phase, all other complexities are removed.

Distance calculation is the process of determining how far an object has traveled, considering different phases of motion like acceleration, constant velocity, and deceleration.
To find the total distance between the two stop signs in the exercise, we add up the distances calculated for each phase:

• 36 meters during acceleration
• 24 meters during constant velocity
• 48 meters during deceleration

The total distance then is \[36m + 24m + 48m = 108m\]. This helps in understanding the complete journey of the car—from stop to stop—elaborating how various motions add up to calculate the entire distance covered.