Question

An a particle travels inside a straight hollow tube 2m 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 ?​

Answer 1

$\large\bf {\orange {\underline { \underline {Gíven}} : - }}$

• distance, s = 2m
• Initial Velocity, u = 1000m/s
• Final Velocity, v = 9000m/s

$\large\bf {\orange {\underline { \underline {Solutíon}} : - }}$

Let 'a' be the uniform acceleration of -particle.

According to Question,

s = 2m,

v = 9000m/s and

u = 1000m/s.

Since,

$\longrightarrow \sf {v}^{2} - {u}^{2} = 2as$

$\longrightarrow \sf {(9000)}^{2} - {(1000)}^{2} = 2a(2)$

$\longrightarrow \sf a = 2 \times {10}^{7} {ms}^{ - 2}$

Let the particle remain in the tube for time 't' then

$\longrightarrow \sf v = u + at$

$\longrightarrow \sf t = \frac{v - u}{a}$

$\longrightarrow \sf t = \frac{9000 - 1000}{2 \times {10}^{7} }$

$\longrightarrow \sf t = 4 \times {10}^{ - 4} s$

Thus,In $\bold{ \sf 4 \times {10}^{ - 4} sec}$the particle in the tube if it enters at a speed of 1000 m/s and leaves at 9000 m/s.