An `alpha` particle travels inside a strainght hollow tube 2m long of a particle acceleration 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?

Options

A. `4 xx 10^(-4) ` sec
B. ` 2xx 10^(-7) ` sec
C. ` 40 xx 10^(-4) ` sec
D. `20 xx 10^(-7)` sec

Explanation

Let a be the uniform acceleration of -particle.
According to the given problem s = 2.0 m,
v = 9000 m/sec and u = 1000 m/sec
Using the formula ` V^(2) = u^(2) + 2 ` as
we have , ` a = (v^(2) - u^(2))/(2s) = ((9000)^(2) - (1000)^(2))/(2xx (2.0)) = (8xx 10^(7))/(4.0) = 2.0 xx 10^(7) "m/sec"^(2)`
Let the particle remains in the tube for t sec.
Then ` V = u + at rArr = (v - u)/(a) rArr (9000 -1000)/(2xx 10^(-7)) = 4xx 10^(-4) ` sec
Hence correct answer is (A)