A particle is moving under the influence of a force given by F=kx, where k is a constant and x is the distance moved. The energy (in joules) gained by the particle in moving from x=0 to x=3 is

Question

A particle is moving under the influence of a force given by F=kx, where k is a constant and x is the distance moved. The energy (in joules) gained by the particle in moving from x=0 to x=3 is (A) 2k (B) 3.5 k (C) 4.5 k (D) 9k

Tardigrade Admin · Accepted Answer

U=(1/2)k(x22-x12) =(1/2)k(32-02) =(9/2)k=4.5 k

Q. A particle is moving under the influence of a force given by $F = k x,$ where $k$ is a constant and $x$ is the distance moved. The energy (in joules) gained by the particle in moving from $x = 0$ to $x = 3$ is

2k

3.5 k

4.5 k

9k

9.5 k

$U = \frac{1}{2} k (x_{2}^{2} - x_{1}^{2})$
$= \frac{1}{2} k (3^{2} - 0^{2})$
$= \frac{9}{2} k = 4.5 k$

Q. A particle is moving under the influence of a force given by F=kx, where k is a constant and x is the distance moved. The energy (in joules) gained by the particle in moving from x=0 to x=3 is

2k

3.5 k

4.5 k

9k

9.5 k

U=21​k(x22​−x12​) =21​k(32−02) =29​k=4.5k

Q. A particle is moving under the influence of a force given by $F = k x,$ where $k$ is a constant and $x$ is the distance moved. The energy (in joules) gained by the particle in moving from $x = 0$ to $x = 3$ is

$U = \frac{1}{2} k (x_{2}^{2} - x_{1}^{2})$
$= \frac{1}{2} k (3^{2} - 0^{2})$
$= \frac{9}{2} k = 4.5 k$