Question

A bullet emerged from a barrel of length 1.2m with a speed of $640ms^{-1}$. Assuming constant acceleration, the approximate time it spends in the barrel after it is fired:
$\text{A.} \ 4 ms$
$\text{B.} \ 400 \mu s$
$\text{C.} \ 40 ms$
$\text{D.} \ 1 s$

Answer 1

Hint: The statement of the question is such that the bullet is fired such that it travels through the barrel (from where bullet exits). Hence initially velocity must be zero, as before firing, there is no velocity associated with the bullet. There after moving with a constant acceleration, it exits the barrel with a velocity of $640ms^{-1}$.

Formula used:
$v=u+at, \ v^2-u^2 = 2as$

Complete answer:
Given $u=0 \ ms^{-1} , \ v=640ms^{-1}$.
Putting in v=u+at, we get
$640 = 0 + at$ . . . .①
Now, for acceleration, we need one more equation, hence using $v^2 - u^2 = 2as$;
And given s=1.2m
Thus, $(640)^2 - 0^2 = 2 a\times 1.2$
Hence we get, $a = \dfrac{640^2}{2.4}ms^{-2}$
Now, putting the acceleration in equation ①, we get;
$t=\dfrac{640}{\dfrac{640^2}{2.4}} = \dfrac{2.4}{640} = 0.00375s = 40 ms$

So, the correct answer is “Option C”.

Additional Information:
The bullet gains speed after the firing from the gun. After the firing, there is some explosion inside the bullet which is due to the gunpowder present inside of the bullet. This powder is basically explosive in nature. The explosion is caused by the friction caused within the molecules of the gunpowder. When the matter of gunpowder is disturbed with huge impact, due to friction between the molecules, the loss in energy gets into sound, light and majorly heat energy. Due to this heat, the gunpowder get ignited and hence explosion occurs.

Note:
Here we have to see what kind of equation of motion will help us to get the values. We can use any set of two equations. One more point to concentrate on is that the calculation of value of acceleration is not that easy to calculate. Hence one should keep it in the form of a fraction and proceed by cutting the terms, which can be cut.