Question

Gexplain (a) Is the distance on a round-trip positive, negative, or zero? (b) Is the displacement on a round-trip positive, negative, or zero?

Short answer

(a) Distance is positive; (b) Displacement is zero.

Step-by-step solution

Understanding Distance for a Round-Trip

Distance is a scalar quantity that measures the total path covered by an object, regardless of its direction. In a round-trip, an object travels from a starting point to a destination and then returns to the starting point. The distance of this trip is the sum of all segments of the path traveled, which means it is always positive.

Evaluating Displacement for a Round-Trip

Displacement is a vector quantity that measures the change in position from the initial point to the final point of an object's travel. In a round-trip, the object returns to its starting point. Therefore, the change in position is zero because the final and initial positions are the same.

Key concepts

Scalar and Vector Quantities

In physics, understanding the difference between scalar and vector quantities is essential. Scalar quantities have only magnitude, meaning they measure the size or amount without considering direction. Examples include distance, speed, and mass. These quantities give us an idea of how much there is, but not which way it's headed.

• Distance: Total path covered without direction.
• Speed: Rate of change of distance.
• Mass: Amount of matter in an object.

On the other hand, vector quantities possess both magnitude and direction. These can describe not just how much there is but also in which direction it is pointing. Common examples include displacement, velocity, and force.

• Displacement: Change in position considering direction.
• Velocity: Speed with direction.
• Force: Push or pull in a specific direction.

Understanding these differences helps in solving problems related to positioning and motion, like calculating journey paths or examining forces at play.

Round-Trip Motion

Round-trip motion involves traveling from one place to another and then back to the starting point. This is a common type of motion where an object or person ends back at the initial position after covering a certain distance in between.

• When considering distance in round-trip motions, it is always positive. This is because distance, being a scalar, simply adds up all the path segments covered regardless of direction.
• Displacement, however, takes into account the starting and ending positions since it is a vector quantity. In a round trip, because the start and end points are the same, the displacement is zero.

Additional real-life examples can include a daily commute to work or taking a leisurely walk along a looped park trail where you return to your starting point. Knowing whether to use distance or displacement in your calculations is key to accurately assessing motion.

Position Change in Physics

Position change, often termed as displacement in physics, describes how an object's location differs from an initial position to a final position. Displacement is a vector quantity, hence direction matters.

• Initial Position: Where the object starts from.
• Final Position: Where the object ends up after movement.
• Magnitude of Displacement: The straight line distance between initial and final positions.
• Direction of Displacement: From initial to final position.

To illustrate, consider walking from home to the store and back. The position initially and finally is home, so your displacement is zero, since displacement measures the shortest path between two points and the start and end are the same.
A firm grasp of position change is crucial in kinematics, helping to predict future motion, calculate velocities, and understand trajectories in various physical systems.