A particle moves in a straight line so that i | vedclass

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

Question

(C) Given the displacement equation: $x^2 = 1 + t^2$.Differentiating both sides with respect to $t$: $2x \frac{dx}{dt} = 2t$,which simplifies to $x v

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) Given the displacement equation: $x^2 = 1 + t^2$.Differentiating both sides with respect to $t$: $2x \frac{dx}{dt} = 2t$,which simplifies to $x v = t$,where $v$ is the velocity.Differentiating $x v = t$ with respect to $t$ using the product rule: $x \frac{dv}{dt} + v \frac{dx}{dt} = 1$.Since $\frac{dv}{dt} = a$ (acceleration) and $\frac{dx}{dt} = v$,we get $x a + v^2 = 1$.Substituting $v = \frac{t}{x}$ into the equation: $x a + (\frac{t}{x})^2 = 1$.$x a = 1 - \frac{t^2}{x^2} = \frac{x^2 - t^2}{x^2}$.Since $x^2 - t^2 = 1$ from the original equation,we have $x a = \frac{1}{x^2}$.Therefore,$a = \frac{1}{x^3} = x^{-3}$.Comparing this with $x^{-n}$,we find $n = 3$.

$A$ particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2 = 1 + t^2$. Its acceleration at any time $t$ is $x^{-n}$ where $n = . . . . .$

Similar Questions

The velocity of a car accelerating uniformly increases from $20 \ m/s$ to $80 \ m/s$ while covering a distance of $200 \ m$. The time taken is $.... \ s$.

What is stopping distance?

$A$ train moves from rest with a uniform acceleration $a$. After attaining a maximum speed $v$,it starts moving with uniform retardation $a$. Assuming $s$ is the total distance covered in the unidirectional motion of the train,find its total time of journey and maximum speed.

$A$ particle starting from rest and moving with constant acceleration travels a distance $x$ in the first $2$ seconds and a distance $y$ in the next $2$ seconds. Then:

$A$ rifle bullet loses $\left(\frac{1}{25}\right)^{th}$ of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is

Vedclass Test Series

Exam Paper Generator

Online Exam Module