Question

A bullet emerges from a barrel of length $1.2m$ with a speed of $640m/s$ . Assuming constant acceleration, the approximate time that spends in the barrel after the gun fired is

• A. $4ms$
• B. $40ms$
• C. $400\mu s$
• D. $1s$

Answer 1

The correct option is A

$4ms$

Step 1: Given data

Barrel length, $s=1.2m$

The initial velocity of the bullet, $u=0m/s$

Final Velocity, $v=640m/s$

Step 2: Formula used

$v^2=u^2+2as$

where, $v$ is the final velocity, $u$ is the initial velocity, $a$ is the acceleration, $s$ is the distance traveled.

Step 3: Find the expression of time required in terms of velocity and acceleration
Accleration is given by, $a=\frac{v-u}{t}$

$$\begin{gathered} a=v/t \\ \Rightarrow t=v/a..........\left(i\right) \end{gathered}$$

Step 4: Find the acceleration of the bullet

$v^2=u^2+2as$

Putting $v=640m/s,u=0m/s,s=1.2m$

$$\begin{gathered} \Rightarrow {640}^2=0^2+2a*1.2 \\ \Rightarrow a=409600/2.4 \\ \Rightarrow a=170667m/s^2..........\left(ii\right) \end{gathered}$$

The acceleration is $170667m/s^2$

Step 5: Find the time spent in the barrel

Using $\left(i\right),\left(ii\right)$ , $t=\frac{640}{170667}=0.0038s\approx 4ms$

Hence the time spent is $4ms$. Option A is correct.