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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

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

Step by step solution

01

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.
02

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

Rubber Ducks A severe storm on January 10, 1992, near the Aleutian Islands, caused a cargo ship to spill 29,000 rubber ducks and other bath toys into the ocean. Ten months later hundreds of rubber ducks began to appear along the shoreline near Sitka, Alaska, roughly \(2600 \mathrm{~km}\) away. What was the approximate average speed, in meters per second, of the ocean current that carried the ducks to shore? (Rubber ducks from the same spill began to appear on the coast of Maine in July 2003.)

Think \& Calculate You drive in a straight line at \(20.0 \mathrm{~m} / \mathrm{s}\) for \(10.0 \mathrm{mi}\), then at \(30.0 \mathrm{~m} / \mathrm{s}\) for another \(10.0 \mathrm{mi}\). (a) Is your average speed \(25.0 \mathrm{~m} / \mathrm{s}\), more than \(25.0 \mathrm{~m} / \mathrm{s}\), or less than \(25.0 \mathrm{~m} / \mathrm{s}\) ? Explain. (b) Verify your answer to part (a) by calculating the average speed.

The initial position of an object that moves with constant velocity is increased. Does this change the intercept or the slope of the position-time graph of the object's motion? Explain.

A golf cart moves with a velocity of \(8 \mathrm{~m} / \mathrm{s}\). Is the displacement of the golf cart from \(t=0\) to \(t=5 \mathrm{~s}\) greater than, less than, or equal to its displacement from \(t=5 \mathrm{~s}\) to \(t=10 \mathrm{~s}\) ? Explain.

In heavy rush-hour traffic you drive in a straight line at \(12 \mathrm{~m} / \mathrm{s}\) for \(1.5 \mathrm{~min}\), then you have to stop for \(3.5 \mathrm{~min}\), and finally you drive at \(15 \mathrm{~m} / \mathrm{s}\) for another \(2.5 \mathrm{~min}\). (a) Plot a position-time graph for this motion. Your graph should extend from \(t=0\) to \(t=7.5 \mathrm{~min}\). (b) Use your graph from part (a) to calculate the average velocity between \(t=0\) and \(t=7.5 \mathrm{~min}\).

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