Question

A particle of charge $q$ and mass $m$ moves along the x-axis under the action of an electric field $E=k-cx$ where $c$ is a positive constant and $x$ is the distance from the point, where the particle was initially at rest. Caluculate:
(a) distance travelled by the particle before it comes to rest.
(b) acceleration at the moment, when it comes to rest.

• A. (a) $\frac{3k}{c}$ (b) $\frac{ql}{m}$
• B. (a) $\frac{2k}{c}$ (b) $\frac{ql}{m}$
• C. (a) $\frac{4k}{c}$ (b) $\frac{3ql}{m}$
• D. (a) $\frac{2k}{c}$ (b) $\frac{2ql}{m}$

Answer 1

The correct option is B (a) $\frac{2k}{c}$ (b) $\frac{ql}{m}$

Charge $=q$

mass $=m$

$E=K-ex$

or, $0=2K-cx$

or, $x=\frac{2K}{c}$

(b) $a=\frac{d^{2}x}{{dt}^2}=\frac{q1}{m}$.