First slide

The 3 equation for uniform acc

Question

Initial speed of an $α$ -particle inside a tube of length 4m is $1 {kms}^{- 1}$ . If it is accelerated in the tube and comes out with a speed of $9 {kms}^{- 1}$ , then the time for which the particle remains inside the tube is

Moderate

A

$8 \times 10^{- 3} s$
B

$8 \times 10^{- 4} s$
C

$80 \times 10^{- 3} s$
D

$800 \times 10^{- 3} s$

Solution

Given, initial speed, $u = 1 {kms}^{- 1} = 1000 {ms}^{- 1}$
Final speed, $v = 9 {kms}^{- 1} = 9000 {ms}^{- 1}$
By using the relation, $v^{2} = u^{2} + 2 as$
$(9000)^{2} = (1000)^{2} + 2 \times a \times 4 \Rightarrow a = 10^{7} {ms}^{- 2}$
$∴$ The time for which the particle remains in the tube
v = u + at
$\Rightarrow t = \frac{v - u}{a} = \frac{9000 - 1000}{10^{7}} = 8 \times 10^{- 4} s$

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