If a particle moves such that the displacemen | vedclass

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

Question

(D) Given that the displacement $s$ is proportional to the square of the velocity $v$,we can write: $s = kv^2$,where $k$ is a constant of proportional

Vedclass · Accepted Answer

$A$ constant

Vedclass · Answer

(D) Given that the displacement $s$ is proportional to the square of the velocity $v$,we can write: $s = kv^2$,where $k$ is a constant of proportionality. Rearranging for $v^2$,we get $v^2 = \frac{1}{k} s$. Let $C = \frac{1}{k}$,so $v^2 = Cs$. Differentiating both sides with respect to time $t$: $\frac{d}{dt}(v^2) = \frac{d}{dt}(Cs)$ $2v \frac{dv}{dt} = C \frac{ds}{dt}$ Since $\frac{dv}{dt} = a$ (acceleration) and $\frac{ds}{dt} = v$ (velocity),we have: $2v a = Cv$ Assuming $v 
eq 0$,we divide by $v$: $2a = C$ $a = \frac{C}{2}$ Since $C$ is a constant,the acceleration $a$ is a constant.

If a particle moves such that the displacement $s$ is proportional to the square of the velocity $v$ acquired,then its acceleration is

Similar Questions

$A$ circular disc of radius $3 \text{ cm}$ is being heated. Due to expansion,its radius increases at the rate of $0.05 \text{ cm/s}$. Find the rate at which its area is increasing when the radius is $3.2 \text{ cm}$.

If a spherical balloon has a variable diameter $3x + \frac{9}{2}$,then find the rate of change of its volume with respect to $x$.

$A$ stone is dropped into a quiet lake and waves move in circles at a speed of $8 \,cm/sec$. At the instant when the radius of the circular wave is $12 \,cm$, how fast is the enclosed area increasing?

$A$ ladder of length $13 \ m$ has one end resting against a vertical wall and the other on the ground. If the lower end moves away from the wall at a speed of $2 \ m/min$, then the speed (in $m/min$) at which the upper end falls when the bottom is $5 \ m$ away from the wall is

If a particle moves in a straight line according to the law $x = a \sin (\sqrt{\lambda} t + b)$, then the particle will come to rest at two points whose distance is [symbols have their usual meaning]

Vedclass Test Series

Exam Paper Generator

Online Exam Module