(D) Given the relation: $t = \sqrt{x} + 3 \implies \sqrt{x} = t - 3 \implies x = (t - 3)^2$.Velocity $v = \frac{dx}{dt} = \frac{d}{dt}(t - 3)^2 = 2(t

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

(D) Given the relation: $t = \sqrt{x} + 3 \implies \sqrt{x} = t - 3 \implies x = (t - 3)^2$.Velocity $v = \frac{dx}{dt} = \frac{d}{dt}(t - 3)^2 = 2(t - 3)$.At $t = 0 \text{ s}$, $v_i = 2(0 - 3) = -6 \text{ m/s}$.At $t = 6 \text{ s}$, $v_f = 2(6 - 3) = 6 \text{ m/s}$.According to the Work-Energy Theorem, the work done $W$ is equal to the change in kinetic energy $\Delta K$.$W = \Delta K = \frac{1}{2}m(v_f^2 - v_i^2)$.Substituting the values: $W = \frac{1}{2}m(6^2 - (-6)^2) = \frac{1}{2}m(36 - 36) = 0 \text{ J}$.

Class 11 Physics Work, Energy, Power and Collision Work Energy Theorem and Conservation of Mechanical Energy

Difficult

The position $x$ of a particle moving in one dimension under the influence of a constant force is given by $t = \sqrt{x} + 3$, where $x$ is in meters and $t$ is in seconds. Find the work done in the first $6$ seconds. (in $\text{ J}$)

A
$1$
B
$2$
C
$3$
D
$0$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Work, Energy, Power and Collision

Subtopic

Work Energy Theorem and Conservation of Mechanical Energy

The figure shows the vertical section of a frictionless surface. $A$ block of mass $2\, kg$ is released from position $A$. Its kinetic energy $(KE)$ as it reaches position $C$ is .............. $J$.

Medium

View Solution

$A$ body of mass $5 \,kg$ is thrown vertically up with a kinetic energy of $490 \,J$. The height at which the kinetic energy of the body becomes half of the original value is (acceleration due to gravity $=9.8 \,ms^{-2}$) (in $\,m$)

EasyKCET 2011

View Solution

$A$ bullet of mass $10 \ g$ is fired with a velocity of $800 \ m/s$. After passing through a mud wall of thickness $1 \ m$,its velocity decreases to $100 \ m/s$. Find the average resistive force exerted by the mud wall in $N$.

Medium

View Solution

$A$ bullet when fired at a target with a velocity of $100\,m/s$ penetrates $1\,m$ into it. If the bullet is fired at a similar target with a thickness of $0.5\,m$,then it will emerge from it with a velocity of:

Medium

View Solution

$A$ heavy stone is thrown with speed $v$ from a cliff of height $h$. How and in which direction should it be thrown so that the stone hits the ground with maximum speed?

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The position $x$ of a particle moving in one dimension under the influence of a constant force is given by $t = \sqrt{x} + 3$, where $x$ is in meters and $t$ is in seconds. Find the work done in the first $6$ seconds. (in $\text{ J}$)

Similar Questions

The figure shows the vertical section of a frictionless surface. $A$ block of mass $2\, kg$ is released from position $A$. Its kinetic energy $(KE)$ as it reaches position $C$ is .............. $J$.

$A$ body of mass $5 \,kg$ is thrown vertically up with a kinetic energy of $490 \,J$. The height at which the kinetic energy of the body becomes half of the original value is (acceleration due to gravity $=9.8 \,ms^{-2}$) (in $\,m$)

$A$ bullet of mass $10 \ g$ is fired with a velocity of $800 \ m/s$. After passing through a mud wall of thickness $1 \ m$,its velocity decreases to $100 \ m/s$. Find the average resistive force exerted by the mud wall in $N$.

$A$ bullet when fired at a target with a velocity of $100\,m/s$ penetrates $1\,m$ into it. If the bullet is fired at a similar target with a thickness of $0.5\,m$,then it will emerge from it with a velocity of:

$A$ heavy stone is thrown with speed $v$ from a cliff of height $h$. How and in which direction should it be thrown so that the stone hits the ground with maximum speed?

Vedclass Test Series

Exam Paper Generator

Online Exam Module