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College Physics (Urone)
Found in: Page 79
College Physics (Urone)

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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Short Answer

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

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.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: 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.

Step 2: 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.

Step 3: 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.

Most popular questions for Physics Textbooks

Dragsters can actually reach a top speed of in only considerably less time than given in Example 2.10 and Example 2.11.

(a) Calculate the average acceleration for such a dragster.

(b) Find the final velocity of this dragster starting from rest and accelerating at the rate found in (a) for 402 m (a quarter mile) without using any information on time.

(c) Why is the final velocity greater than that used to find the average acceleration?

Hint: Consider whether the assumption of constant acceleration is valid for a dragster. If not, discuss whether the acceleration would be greater at the beginning or end of the run and what effect that would have on the final velocity.

What is the last thing you should do when solving a problem? Explain.

The North American and European continents are moving apart at a rate of about 3 cm/y. At this rate how long will it take them to drift 500 km farther apart than they are at present?

A soft tennis ball is dropped onto a hard floor from a height of \[{\bf{1}}.{\bf{50}}{\rm{ }}{\bf{m}}\] and rebounds to a height of\[{\bf{1}}.{\bf{10}}{\rm{ }}{\bf{m}}\]. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) Calculate its acceleration during contact with the floor if that contact lasts\[{\bf{3}}.{\bf{50}}{\rm{ }}{\bf{ms}}{\rm{ }}\left( {{\bf{3}}.{\bf{50}} \times {\bf{1}}{{\bf{0}}^{ - {\bf{3}}}}{\bf{s}}} \right)\]. (d) How much did the ball compress during its collision with the floor, assuming the floor is absolutely rigid?

A kangaroo can jump over an object 2.50 m high.

(a) Calculate its vertical speed when it leaves the ground.

(b) How long is it in the air?
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