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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 (\(Δx\)) divided by the change in time (\(Δt\)). The formula for velocity is given by \(v = \frac{Δx}{Δt}\).
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 (\(Δt\)). In mathematical terms, it is represented as \(s = \frac{d}{Δt}\).
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 \(s = \frac{10m}{Δt}\) (assuming some time, \(Δt\)). However, the vector displacement is 0 (as the object returned to its starting position), so the average velocity (\(v\)) of the object is \(v = \frac{0}{Δt}\) = 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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Most popular questions from this chapter

When can the speed and average speed of a vehicle be equal?

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Name the physical quantity that measures fastness or slowness of a moving object.
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