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

$A$ particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x$-axis. Identify all figures that correctly represent the motion qualitatively. ($a =$ acceleration,$v =$ velocity,$x =$ displacement,$t =$ time)

$A$ particle moves in a straight line with a constant acceleration. It changes its velocity from $10 \, m/s$ to $20 \, m/s$ while passing through a distance of $135 \, m$ in $t$ seconds. The value of $t$ is..........$s$.

$A$ particle starts from the origin at time $t=0$ and moves in the positive $x$-direction. Its velocity $v$ varies with time as $v=10t \text{ cm/s}$. The distance covered by the particle in $8 \text{ s}$ will be: (in $\text{ cm}$)

$A$ particle with initial velocity $v_0$ moves with constant acceleration $a$ in a straight line. Find the distance travelled in the $n^{th}$ second.

What is stopping distance?

Vedclass Test Series

Exam Paper Generator

Online Exam Module