/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q12CQ How are instantaneous velocity a... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

How are instantaneous velocity and instantaneous speed related to one another? How do they differ?

Short Answer

Expert verified

The velocity of the object at an instant is called instantaneous velocity. As the time interval approaches 0, so does the distance traveled. The instantaneous speed is the non-zero limit of the distance-to-time ratio.

Step by step solution

01

Instantaneous Velocity

The velocity of an item at a given point in time. The instantaneous velocity is "the velocity of an item in motion at a single point in time."

The instantaneous velocity of an item with uniform velocity could be the same as its average velocity.

Graph showing average and instantaneous velocity.

It's calculated in the same way as average velocity but with a shorter time period. We know that total displacement divided by total time equals average velocity for a particular time span.

The displacement approaches 0 as the time interval approaches zero. However, the ratio of displacement to time has a non-zero limit, which is known as instantaneous velocity.

02

Instantaneous speed

We know that the entire distance traveled divided by the total time taken equals the average speed for a given time span.

The distance traveled approaches 0 as the time interval approaches zero. However, the instantaneous speed is the non-zero limit of the distance-to-time ratio. We may also say that instantaneous speed at any given moment is the magnitude of instantaneous velocity at that time, to put it another way.

03

Difference between instantaneous speed and velocity

Instantaneous speed

Instantaneous velocity

It is a scalar quantity

It is a vector quantity

It is only the magnitude of the speed at instants.

It is the value of velocity magnitude as well as the direction of the body at instants.

Therefore, the instantaneous velocity is the velocity of an item at a specific point in time. The distance traveled decreases as the specified interval of time approaches zero. The non-zero range of the distance-to-time ratio is the instantaneous speed.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The severity of a fall depends on your speed when you strike the ground. All factors but the acceleration due to gravity being the same, how many times higher could a safe fall on the Moon be than on Earth (gravitational acceleration on the Moon is about 1/6 that of the Earth)?

(a) Calculate Earth’s average speed relative to the Sun.

(b) What is its average velocity over a period of one year?

a) Explain how you can use the graph of position versus time in Figure 2.54 to describe the change in velocity over time.

Identify

(b) the time ( ta, tb , tc , td , or te ) at which the instantaneous velocity is greatest,

(c) the time at which it is zero, and

(d) the time at which it is negative.

Figure 2.54

(a) By taking the slope of the curve in Figure 2.60, verify that the velocity of the jet car is\({\bf{115}}{\rm{ }}{\bf{m}}/{\bf{s}}\)at\(t = {\rm{ }}{\bf{20}}{\rm{ }}{\bf{s}}\). (b) By taking the slope of the curve at any point in Figure 2.61, verify that the jet car’s acceleration is\({\bf{5}}.{\bf{0}}{\rm{ }}{\bf{m}}/{{\bf{s}}^{\bf{2}}}\).

a) A light-rail commuter train accelerates at a rate of\({\bf{1}}{\bf{.35}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\). How long does it take to reach its top speed of 80.0 km/h, starting from rest? (b) The same train ordinarily decelerates at a rate of\({\bf{1}}{\bf{.65}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\). How long does it take to come to a stop from its top speed? (c) In emergencies the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.30 s. What is its emergency deceleration in\({\bf{m/}}{{\bf{s}}^{\bf{2}}}\)?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.