Question

A bullet comes out of the barrel of a gun of length 2 m with a speed\[80m{s^{ - 1}}\]. Find the average acceleration of the bullet.
A. \[1.6\,m{s^{ - 2}}\]
B. \[160\,m{s^{ - 2}}\]
C. \[1600\,m{s^{ - 2}}\]
D. \[16\,m{s^{ - 2}}\]

Answer 1

Hint: In order to start with the problem, we need to know about the acceleration and it works on Newton’s second law. The acceleration is the rate of change of velocity of a body. Newton’s second law speaks about the mass and the acceleration of a body. It depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object increases, then the acceleration of the object also increases. But as the mass of an object increases, the acceleration of the object decreases.

Formula Used:
The equation of motion is given by,
\[{v^2} = {u^2} + 2as\]
Where, v is final velocity, u is initial velocity, a is acceleration and s is displacement.

Complete step by step solution:
When a bullet comes out of a gun with a speed of \[80m{s^{ - 1}}\]of length (displacement) 2m. Then, we need to find the average acceleration of the bullet. From the equation of motion, we have the formula as,
\[{v^2} = {u^2} + 2as\]
\[\Rightarrow {80^2} = 0 + 2 \times a \times 2\]
\[\Rightarrow {80^2} = 4a\]
\[\Rightarrow a = \dfrac{{6400}}{4}\]
\[\therefore a = 1600\,m{s^{ - 2}}\]
Therefore, the average acceleration of the bullet is \[1600\,m{s^{ - 2}}\].

Hence, Option C is the correct answer.

Note:Since the value of force is not given, we cannot find the acceleration of the bullet using Newton's second law that is,\[F = ma\]. So, we need to use the equation of motion to find the acceleration of the bullet where the final velocity and the displacement are given.