/*! 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} Problem 38 A particle is moving along strai... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 38

A particle is moving along straight line with initial velocity \(+7 \mathrm{~m} / \mathrm{sec}\) and uniform acceleration \(-2 \mathrm{~m} / \mathrm{sec}^{2}\). The distance travelled by the particle in \(4^{\text {th }}\) second of its motion is : (1) zero (2) \(0.25 \mathrm{~m}\) (3) \(0.5 \mathrm{~m}\) (4) \(7 \mathrm{~m}\) (5) \(0.75 \mathrm{~m}\)

Short Answer

Expert verified
The distance traveled in the 4th second is 0 m.

Step by step solution

01

Understand the Problem

A particle moves with an initial velocity of \(+7 \, \text{m/s}\) and has a uniform acceleration of \(-2 \, \text{m/s}^2\). We need to determine the distance traveled in the 4th second of its motion.
02

Identify the Formula

To solve this, use the formula for distance traveled in the nth second: \[ S_n = u + a(n - 0.5) \] where \(S_n\) is the distance traveled in the nth second, \(u\) is the initial velocity, \(a\) is the acceleration, and \(n\) is the specific second.
03

Substitute the Given Values

For the 4th second (n = 4), initial velocity \(u = +7 \, \text{m/s}\), and acceleration \(a = -2 \, \text{m/s}^2\), substitute the values into the formula: \[ S_4 = 7 + (-2)(4 - 0.5) \]
04

Solve the Equation

Calculate it step-by-step: 1. Calculate \(4 - 0.5\): \[ 4 - 0.5 = 3.5 \] 2. Multiply by acceleration \[ -2 \times 3.5 = -7 \] 3. Add the initial velocity \[ 7 + (-7) = 0 \]
05

Conclude the Result

The calculated distance traveled in the 4th second is \(0 \, \text{m}\). Thus, the correct answer is option (1).

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 91影视!

Key Concepts

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

kinematics
Kinematics is a branch of physics that deals with the motion of objects without considering the forces that cause the motion. It focuses on the position, velocity, and acceleration of objects. When studying kinematics, you typically use equations of motion to describe how objects move. These equations can help you predict where an object will be at a given time or how fast it will be moving.
uniform acceleration
Uniform acceleration refers to a constant acceleration, meaning the object's velocity changes at a constant rate over time. An important concept here is the relationship between velocity, acceleration, and time. If an object has a uniform acceleration, we can use specific equations of motion to describe its behavior. These include:
  • Final velocity: \(v = u + at\)
  • Distance traveled: \(d = ut + \frac{1}{2}at^2 \)
  • Distance in nth second: \(S_n = u + a(n - 0.5) \)

Understanding these equations allows you to solve various problems related to uniformly accelerating objects.
initial velocity
The initial velocity (denoted as \(u\)) is the velocity at which an object starts its motion. This is a crucial parameter because it affects how the object moves over time. In kinematic problems, knowing the initial velocity is essential for predicting future position and velocity. For instance, in our problem:
  • Initial velocity (u): \(u = +7 \text{m/s}\)

    • It influenced the calculation of distance traveled in the fourth second.

By understanding initial velocity, you can better understand an object's motion from the start point.

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 correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are) (1) Adsorption is always exothermic (2) Physisorption may transform into chemisorption at high temperature (3) Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature (4) Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation.

A particle is projected from this satellite radially outward relative to satellite with speed \(u\). Find the minimum value of \(u\) so that particle escape from the gravitational force of earth. (Mass of earth \(>>>\) mass of satellite \(>>>\) mass of particle) (1) \(\sqrt{\frac{G M}{R}}\) (2) \(\sqrt{\frac{G M}{2 R}}\) (3) \(\sqrt{\frac{2 G M}{R}}\) (4) \(2 \sqrt{\frac{G M}{R}}\)

STATEMENT-1: Drift velocity is the average velocity which is aqiured by electron due to electric field applied by source. STATEMENT-2 : Drift velocity is independent of temperature. (1) Statement- 1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (2) Statement- 1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (3) Statement- 1 is True, Statement-2 is False (4) Statement- 1 is False, Statement-2 is True.

The vapour pressure of the solution of two liquids \(\mathrm{A}\left(\mathrm{p}^{\circ}=80 \mathrm{~mm}\right)\) and \(\mathrm{B}\left(\mathrm{p}^{\circ}=120 \mathrm{~mm}\right)\) is found to be \(100 \mathrm{~mm}\) when \(\mathrm{x}_{\mathrm{A}}=0.4\). The result shows that : (1) solution exhibits ideal behaviour (2) \(\Delta \mathrm{H}_{\text {solution }}<0\) (3) solution shows negative deviations (4) solution will show positive deviations for lower concentration and negative deviations for higher concentrations.

Let \(z_{1}\) and \(z_{2}\) be \(n^{\text {th }}\) roots of unity which subtends a right angle at the origin then 'n' must be of the form - (1) \(4 \mathrm{~K}+1, \mathrm{~K} \in \mathrm{I}\) (2) \(4 \mathrm{~K}+2, \mathrm{~K} \in \mathrm{I}\) (3) \(4 \mathrm{~K}+3, \mathrm{~K} \in \mathrm{I}\) (4) \(4 \mathrm{~K}, \mathrm{~K} \in \mathrm{I}\) (5) None of these
See all solutions

Recommended explanations on English Textbooks

Language Acquisition

Read Explanation

5 Paragraph Essay

Read Explanation

Rhetorical Analysis Essay

Read Explanation

English Grammar Summary

Read Explanation

English Grammar

Read Explanation

TESOL (English)

Read Explanation
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.