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Deceleration is what happens when an object slows down. In this exercise, the runner is slowing down while nearing the finish line. This is important to understand because it directly affects the time it will take her to reach the stop.
When we talk about deceleration, it is seen as a negative acceleration. This means the speed of the object decreases as it moves forward. In our exercise, the runner's deceleration is given as -0.5 m/s². This value tells us how much the speed reduces each second. So, the runner's speed decreases by 0.5 meters per second, every second.

• Deceleration is a negative change in velocity per unit time.
• It tells us how quickly an object is coming to a stop or reducing its speed.

Understanding deceleration helps us calculate how long it might take for any moving object, like our runner, to come to a full stop. This concept is used in various practical situations, such as planning safe stopping distances for vehicles.

Equations of motion help us understand how objects move under the force of gravity and other influences, like deceleration. They allow us to predict future positions and velocities of moving objects using math.
In the given problem, one of these equations,

• \[v^2 = u^2 + 2as\]

allows us to calculate aspects of the runner's movement as she decelerates. Here:

• \(v\) is the final velocity (0 m/s, when she stops)
• \(u\) is the initial velocity (8 m/s)
• \(a\) is the acceleration, which is given as a negative value because it's deceleration (-0.5 m/s²)
• \(s\) is the distance over which the runner decelerates (75 m)

This equation helps explain how these factors interact to bring the runner to a stop. The equations of motion are fundamental tools in kinematics, aiding us in understanding how different factors affect the movement of objects across different scenarios.

Velocity is how fast something is moving and the direction it is moving in. In the context of this exercise, the runner's initial velocity is 8 m/s, which means she is traveling at a speed of 8 meters per second towards the finish line.
Velocity is different from speed. While speed gives us a number that tells us how fast something moves, velocity also adds the direction. This distinction is particularly significant when considering changes in motion, like our runner's deceleration.

• Initial velocity is the speed at which the runner starts from a given point.
• Final velocity occurs when the runner stops, reaching 0 m/s in this case.
• Changes in velocity (due to deceleration in this case) affect how long it will take to cover a distance.

This concept of velocity is crucial for understanding motion scenarios. In problems like these, knowing the initial and final velocities can help calculate time, distance, and changes in the object's state of motion effectively.