Question

A charged particle travels along the inside of a straight hollow tube $2.0$ metre long. The particle is uniformly accelerated. What is the time spent by the particle in the tube if it enters at a speed of $1000$m s and leaves at $9000$ m/s.

• A. $2\times {10}^{-4}$ seconds
• B. $5\times {10}^{-4}$ seconds
• C. $4\times {10}^{-4}$ seconds
• D. $2.5\times {10}^{-4}$ seconds

Answer 1

The correct option is C $4\times {10}^{-4}$ seconds

$v=9000m/s,u=1000m/s,s=2m$

Applying $3^{rd}e{q}^n$ of motion, $v^2-u^2=2s$

$\Rightarrow (9000{)}^2-(1000{)}^2=2\left(a\right)\left(2\right)$

$\Rightarrow a=2\times {10}^{7}m/s^2$

Applying $1^{st}e{q}^n$ of motion, $v=u+at$

$9000=1000+(2\times {10}^7)t$

$t=\frac{8\times {10}^3}{2\times {10}^7}=4\times {10}^{-4}sec$ (C)