A point moves in a straight line under the retardation a $v^{2}$, where ' $a$ ' is a positive constant and $v$ is speed. If the initial speed is $u$, the distance covered in ' $t$ ' seconds is
in Physics
31 views
3 Votes
3 Votes
A point moves in a straight line under the retardation a $v^{2}$, where ' $a$ ' is a positive constant and $v$ is speed. If the initial speed is $u$, the distance covered in ' $t$ ' seconds is:

(A) a ut

(B) $\frac{1}{a} \log (a u t)$

(C) $\frac{1}{a} \log (1+a u t)$

(D) $a \log (a u t)$
in Physics
by
4.3k Points

1 Answer

2 Votes
2 Votes
 
Best Answer
The retardation is given by $\frac{d v}{d t}=-a v 2$ integrating between proper limits

$$

\begin{array}{l}

\Rightarrow \quad-\int_{u}^{v} \frac{d v}{v^{2}}=\int_{0}^{t} a d t \\

\text { or } \quad \frac{1}{v}=a t+\frac{1}{u} \\

\Rightarrow \quad \frac{d t}{d x}=a t+\frac{1}{u} \Rightarrow d x=\frac{u d t}{1+a u t}

\end{array}

$$

integrating between proper limits

$$

\begin{array}{ll}

\Rightarrow & \int_{0}^{s} d x=\int_{0}^{1} \frac{u d t}{1+a u t} \\

\Rightarrow & S=\frac{1}{a} \ln (1+a u t)

\end{array}

$$
Edited by
by
4.3k Points

Related Questions

Welcome To Informesia

Informesia Helps You To Prepare India's All States Board Exams (CBSE, ICSE, UP Board, BSEB, HPBOSE, RBSE, MSBSHSE) and Competitive Exam Like JEE (Main + Advanced), AIIMS, NEET, KVPY, NTSE, BITSAT, Olympiad, CLAT...etc.
For Any Query or Suggestion, Please Contact us on :
[email protected]

Connect us on Social Media