An α particle travels inside a straight hollow tube 2 m long of a particle accelerator under uniform acceleration.

Q: An α particle travels inside a straight hollow tube 2 m long of a particle accelerator under uniform acceleration. How long is the particle in the tube if it enters at a speed of 1000 m/s and leaves at 9000 m/s. what is its acceleration during this interval ?
Sol: Let ‘a’ be the uniform acceleration of α – particle .

According to given problem s = 2 m,

V = 9000 m/s and u = 1000 m/s.

Since v² – u² = 2 a S

(9000)² -(1000)² = 2a (2)

⇒ a =2 × 10⁷ m/s²

Let the particle remains in the tube for time ‘t’, then v = u + at

$\large t = \frac{v-u}{a} = \frac{9000-1000}{2 \times 10^7}$

= 4 × 10⁷ sec