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Chapter 2: Problem 59

Define velocity and explain how it is different from speed.

Short Answer

Expert verified
Answer: The main difference between velocity and speed is that velocity is a vector quantity, which includes both the rate of displacement and the direction of movement, while speed is a scalar quantity, representing only the rate of distance covered without considering direction. Direction plays a crucial role in distinguishing the two concepts, as velocity accounts for direction, while speed does not.

Step by step solution

01

Define Velocity

Velocity is the rate of change of an object's position (displacement) with respect to time. It is a vector quantity, meaning it has both magnitude and direction. In mathematical terms, velocity (\(v\)) is represented by the change in position (\(螖x\)) divided by the change in time (\(螖t\)). The formula for velocity is given by \(v = \frac{螖x}{螖t}\).
02

Define Speed

Speed is the rate of change of an object's distance with respect to time. It is a scalar quantity, meaning it only has magnitude and no direction. Similar to velocity, the formula for speed (\(s\)) is given by the change in distance (\(d\)) divided by the change in time (\(螖t\)). In mathematical terms, it is represented as \(s = \frac{d}{螖t}\).
03

Describe the Key Difference Between Velocity and Speed

The main difference between velocity and speed is that velocity is a vector quantity while speed is a scalar quantity. This means that velocity includes both the rate of displacement and the direction of movement, while speed only considers the rate of distance covered, without any regard to direction.
04

Provide an Example

Consider an object that moves 5 meters to the East and then 5 meters to the West. The total distance covered is 10 meters, so the average speed (\(s\)) of the object is \(s = \frac{10m}{螖t}\) (assuming some time, \(螖t\)). However, the vector displacement is 0 (as the object returned to its starting position), so the average velocity (\(v\)) of the object is \(v = \frac{0}{螖t}\) = 0. This example highlights the difference between speed and velocity, with speed providing a measure of how fast an object moves, and velocity describing both the rate of displacement and direction of movement.

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Key Concepts

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

Speed
In the realm of physics, speed is an essential concept that describes how fast something is moving. When you think about speed, you are considering how much ground an object covers over a given period of time. It doesn't matter in which direction the object is moving, just how quickly it is doing so.
  • Speed is expressed mathematically as the change in distance divided by the change in time, commonly noted as \(s = \frac{d}{螖t}\).
  • It is important to note that speed is considered a scalar because it only reflects magnitude 鈥� the actual amount 鈥� and not direction.
Whether you are driving a car or watching a sprinter in a race, it is the speed that tells you exactly just how fast you are going.
Vector quantity
Vector quantities are a cornerstone in physics, providing depth to our understanding of movement and forces. When we say something is a vector quantity, we are talking about attributes that are not just defined by magnitude, but also bear direction.
  • Common examples of vector quantities include velocity, force, and acceleration.
  • Represented graphically, vectors are often depicted as arrows, where the length of the arrow shows the magnitude and the arrowhead points in the direction.
This dual characteristic of vectors allows them to effectively describe scenarios where the direction is crucial for understanding the context.
Scalar quantity
Scalar quantities offer simplicity by focusing solely on the magnitude aspect. Whenever you explore phenomena that do not involve direction, scalars are often the most informative.
  • Examples of scalar quantities include speed, temperature, mass, and time.
  • Unlike vectors, they are sufficient for calculations where direction is inconsequential.
While watching a clock or measuring temperature, scalars can tell you exactly what you need to know without any added complexity of direction.
Displacement
Displacement gives us a more precise understanding of movement by looking at how far an object is from its starting point, factoring in the direction. This makes it different from distance, which only asks, "How much ground was covered?"
  • In mathematical terms, displacement is a vector, meaning it has both magnitude and direction, akin to a straight line from start to finish.
  • The difference between the initial and final positions of an object is referred to as the displacement.
Whether you're planning a shortcut home or studying an object's movement in physics, displacement offers a complete narrative beyond just the distance traveled.

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Most popular questions from this chapter

A simple pendulum was given to a physics student to determine its time period. Arrange the following steps in sequential order to determine its time period. (a) Calculate the radius of the bob ' \(R\) ' by dividing the diameter by 2 . (b) Take a metre scale and measure the length of the string from the point of suspension to the lower tip of the bob \((\ell)\). (c) Place the bob over a meter scale and hold it in position with two wooden blocks or stiff cardboards. Measure the diameter (D) of the bob. (d) Now, the length of the pendulum ( \(\ell\) ) is given by \(\left(\ell_{1}-\mathrm{R}\right)\). (e) Consider the formula \(\mathrm{T}=2 \pi . \sqrt{\frac{\ell}{g}}\) Calculate the time period of the simple pendulum. (1) abcde (2) edcba (3) bcade (4) deabc

A lorry driver sees a old man crossing the road. Suddenly he applies brakes and stops the lorry within \(30 \mathrm{~s}\). If the initial speed of the lorry is \(108 \mathrm{~km} \mathrm{~h}^{-1}\), find its deceleration.

"Slow and fast are relative". Explain it with examples.

What is an odometer and a speedometer?

Find the relationship between the time period of the pendulum and the length of the pendulum.
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