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Chapter 2: Problem 5

Analyze Is it possible for you to take a hike and have the distance you cover be equal to the magnitude of your displacement? If yes, give an example to justify your answer.

Short Answer

Expert verified
Yes, if you travel in a straight line. For example, hiking 3 km straight from your home to a point is equal in distance and displacement.

Step by step solution

01

Understanding Distance and Displacement

First, let's clarify the concepts. Distance is the total length of the path traveled, while displacement is the shortest straight line from the start to the endpoint. Displacement is a vector quantity having both magnitude and direction, whereas distance is a scalar quantity having only magnitude.
02

Analyzing the Condition

For the distance to be equal to the magnitude of displacement, the path traveled must be a straight line without any turns or deviations. This condition ensures that the total path length (distance) is the same as the direct straight-line measurement from the start to the finish point (displacement).
03

Providing an Example

Imagine you decide to hike from your home to a friend's house, and the path is a straight road with no turns. If the shortest path you can take is 3 kilometers straight to your friend's house, then both your distance traveled and the magnitude of your displacement will be 3 kilometers.

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Key Concepts

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

Distance
When we talk about distance in physics, we're referring to the total length of the path traveled by an object. It's akin to the number of steps your fitness tracker logs regardless of your direction.
Distance is a scalar quantity, which means it has only magnitude and no direction. This concept is quite similar to tracking mileage in your car.
  • If you drive in a loop and return to your starting point, your distance may be high, but your displacement is zero.
  • Distance only considers the length of the journey, ignoring where you start and end.
Understanding the difference between scalar and vector quantities is crucial in physics. More on that later!
Displacement
Displacement, on the other hand, measures how far, in a straight line and in what direction, an object ends up from its starting position. It's like drawing a straight line from where your morning jog began to where it ended.
Displacement is a vector quantity because it includes both a magnitude (like distance) and a direction (like north, south, east, or west).
For example:
  • If you walk 3 km north, then 3 km south, your distance would be 6 km but your displacement would be 0 km, since you end up at your starting point.
  • If you move 5 km east without changing direction, your distance equals your displacement.
Being aware that displacement takes into account direction will help you distinguish it from distance.
Vector Quantity
Vector quantities are key concepts in physics. They are defined by having both a magnitude and a direction.
Think of them as instructions that not only tell you how far to go, but also where to go. Velocity, force, and displacement are common vector quantities in physics.
  • Magnitude tells you how big or massive the vector is.
  • Direction tells you where the vector is pointing.
By combining these two components, vectors provide a fuller description of physical phenomena compared to scalar quantities. In exercises and real-life scenarios, knowing direction can change the outcome entirely!
Scalar Quantity
Scalar quantities are simpler in nature than vectors. They only provide a magnitude and leave out the direction.
Examples of scalar quantities include distance, speed, mass, and time鈥攁ll providing a numerical value that tells you 'how much'.
  • A temperature reading of 25掳C or the distance of 10 miles only needs a number to convey useful information.
  • In these cases, direction is not necessary for understanding the quantity.
Recognizing the different applications between scalar and vector quantities helps make sense of complex physics problems by simplifying the components you need to consider.

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Most popular questions from this chapter

Calculate A golfer putts on the eighteenth green at a distance of \(5.0 \mathrm{~m}\) from the hole. The ball rolls straight, in the positive direction, but overshoots the hole by \(1.2 \mathrm{~m}\). The golfer then putts back to the hole and sinks the putt for par. (a) What is the distance traveled by the ball? (b) What is the displacement of the ball?

Cleo the black lab runs to pick up a stick on the ground at the location \(x=3.0 \mathrm{~m}\). The equation of motion for Cleo is \(x=-12.1 \mathrm{~m}+(5.2 \mathrm{~m} / \mathrm{s})\) t. (a) Where is Cleo at \(t=1.6 \mathrm{~s}\) ? (b) At what time does Cleo reach the stick?

You jog at \(9.50 \mathrm{~km} / \mathrm{h}\) for \(8.00 \mathrm{~km}\); then you jump into a car and ride an additional \(16.0 \mathrm{~km}\). What average speed must the car have for the average speed for the entire \(24.0-\mathrm{km}\) trip to be \(22.0 \mathrm{~km} / \mathrm{h}\) ?

Calculate In 2009, Usain Bolt of Jamaica set a world record of \(9.58 \mathrm{~s}\) in the \(100-\mathrm{m}\) dash. What was his average speed? Give your answer in meters per second and kilometers per hour.

You are riding in a car on a straight stretch of a two-lane highway with a speed of \(26 \mathrm{~m} / \mathrm{s}\). At a certain time, which we will choose to be \(t=0\), you notice a truck moving toward you in the other lane. The truck has a speed of \(31 \mathrm{~m} / \mathrm{s}\) and is \(420 \mathrm{~m}\) away at \(t=0\). (a) Write the position-time equations of motion for your car and for the truck in the other lane. (b) Plot the two equations of motion on a position-time graph. (c) At what time do you and the truck pass one another, going in opposite directions?
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