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Chapter 1: Problem 9

What is the distinction between speed and velocity? Describe a situation in which an object's speed is constant but its velocity is not.

Short Answer

Expert verified
Question: Explain the difference between speed and velocity and provide a situation in which an object has constant speed but its velocity is changing. Answer: Speed is a scalar quantity representing the rate at which an object covers distance, having only magnitude and no direction. Velocity is a vector quantity representing the displacement of an object per unit time, considering both magnitude and direction. A situation in which an object has constant speed but changing velocity is a car moving in a circular path with constant speed, as its direction continuously changes, causing its velocity vector to change too.

Step by step solution

01

Understanding Speed and Velocity

Speed is a scalar quantity that represents the rate at which an object covers distance in any direction. It is calculated as the distance traveled divided by the time taken to travel that distance. Speed has only magnitude but no direction. On the other hand, velocity is a vector quantity that represents the displacement of an object per unit time, taking both magnitude and direction into consideration. Mathematically, speed is given by the formula: speed = distance / time Velocity is given by the formula: velocity = displacement / time Despite being related, speed and velocity are not the same because velocity takes direction into account, while speed does not.
02

Example Situation

Consider a car moving in a circular path with a constant speed. In this situation, the car's speed is constant because it is covering an equal distance in equal intervals of time. However, its velocity is constantly changing due to the change in direction as it moves along the circular path. Since the direction of the car is changing at every point on the circle, the direction of its velocity vector keeps changing too. A change in the direction of the velocity vector signifies that the object's velocity is not constant, even though its speed remains the same.

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Most popular questions from this chapter

Two rectangular rugs are on display in a showroom. If one rug is twice as long as the other, does this necessarily mean that its area is also twice as large as that of the second? Explain.

Can the resultant of two velocities have zero magnitude? If so, give an example.

A wind is blowing from the north (the air is moving toward the south). When a person is walking toward the north, is the relative speed of the wind that the person senses greater than, the same as, or less than the speed the person senses when not walking? How about when the person is walking toward the south?

As a stop light changes from red to green, a car starts to cross through the intersection. An instant before it begins to move, its velocity is zero. Must its acceleration at that time also be zero. Why or why not? Explain.

What does the slope of a distance-versus-time graph represent physically?
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