In some appropriate units,the time (t) and po | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the relation: $t = x^2 + x$. Differentiating both sides with respect to $x$: $\frac{dt}{dx} = 2x + 1$. Since velocity $v = \frac{dx}{dt}$,we

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Given the relation: $t = x^2 + x$. Differentiating both sides with respect to $x$: $\frac{dt}{dx} = 2x + 1$. Since velocity $v = \frac{dx}{dt}$,we have $\frac{1}{v} = 2x + 1$,which implies $v = (2x + 1)^{-1}$. Acceleration $a$ is given by $a = v \frac{dv}{dx}$. Differentiating $v$ with respect to $x$: $\frac{dv}{dx} = -1(2x + 1)^{-2} 	imes 2 = -2(2x + 1)^{-2}$. Substituting $v$ and $\frac{dv}{dx}$ into the acceleration formula: $a = (2x + 1)^{-1} 	imes [-2(2x + 1)^{-2}]$. Therefore,$a = -2(2x + 1)^{-3} = -\frac{2}{(2x + 1)^3}$.

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

Similar Questions

$A$ $150 \,m$ long train is moving with a uniform velocity of $45 \,km/h$. The time taken by the train to cross a bridge of length $850 \,m$ is..........$sec$.

When will the average acceleration and instantaneous acceleration of a particle be equal over any time interval?

$A$ particle starting from rest moves with a uniform acceleration and covers $x$ meters in the first $5 \ s$. The same particle will cover the following distance in the next $5 \ s$:

The displacement and the increase in the velocity of a moving particle in the time interval of $t$ to $(t+1) s$ are $125 \ m$ and $50 \ m/s$,respectively. The distance travelled by the particle in $(t+2)^{th} s$ is . . . . . . $m$.

The position $x$ of a particle at any instant is related to its velocity $v$ by the equation $v = \sqrt{2x + 9}$. The particle starts from the origin. What are the initial acceleration and initial velocity of the particle?

Vedclass Test Series

Exam Paper Generator

Online Exam Module