In some appropriate units, time $(t)$ and position $(x)$ relation of a moving particle is given by $t=x^2+x$. The acceleration of the particle is

Q.16) In some appropriate units, time $(t)$ and position $(x)$ relation of a moving particle is given by $t = x^{2} + x$ . The acceleration of the particle is

A) $+ \frac{2}{2 x + 1}$

B) $- \frac{2}{(x + 2)^{3}}$

C) $- \frac{2}{(2 x + 1)^{3}}$

D) $+ \frac{2}{(x + 1)^{3}}$

Answers (1)

Solution:
Given: $t = x^{2} + x \Rightarrow x (t)$
Differentiate to get velocity:

$\frac{d t}{d x} = 2 x + 1 \Rightarrow \frac{d x}{d t} = \frac{1}{2 x + 1}$
Differentiate again for acceleration:

$a = \frac{d^{2} x}{d t^{2}} = \frac{d}{d t} (\frac{1}{2 x + 1})$
Using chain rule:

$\frac{d}{d t} = \frac{d}{d x} \cdot \frac{d x}{d t}$
So,

$a = \frac{d}{d x} (\frac{1}{2 x + 1}) \cdot \frac{1}{2 x + 1} = (\frac{- 2}{(2 x + 1)^{2}}) \cdot \frac{1}{2 x + 1} = \frac{- 2}{(2 x + 1)^{3}}$
Hence, the answer is option (3) $- 2 / (2 x + 1)^{3}$ .

Exams

Colleges

Predictors

Resources

Quick links

Quick Links

Exams

Colleges

Resources

Colleges

Resources

Exams

Exams

Colleges

Resources

Diploma Colleges

Other Exams

Exams

Resources

Upcoming Events

Exams

Top Schools

Products & Resources

NCERT Study Material

Top Countries

Resources

Exams

Colleges

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges & Courses

Predictors

Resources

Law Preparation

MBA Preparation

Engineering Preparation

Medical Preparation

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Predictors

Resources

Resources

Exams

Colleges

Predictors & E-Books

Exams

Predictors & Articles

Colleges

Resources

Exams

Colleges

Resources

Top Courses & Careers

Colleges

Exams

Resources

Get Answers to all your Questions

Q.16) In some appropriate units, time (t) and position (x) relation of a moving particle is given by t=x2+x. The acceleration of the particle is A) +22x+1 B) −2(x+2)3 C) −2(2x+1)3 D) +2(x+1)3

Answers (1)

Posted by

Dimpy

NEET 2024 Most scoring concepts

Similar Questions

Trending Articles/News

Latest Question

Ask your Query

Welcome Back :)

Register to post Answer

Welcome Back :)

Q.16) In some appropriate units, time $(t)$ and position $(x)$ relation of a moving particle is given by $t = x^{2} + x$ . The acceleration of the particle is

A) $+ \frac{2}{2 x + 1}$

B) $- \frac{2}{(x + 2)^{3}}$

C) $- \frac{2}{(2 x + 1)^{3}}$

D) $+ \frac{2}{(x + 1)^{3}}$