Question

The velocity of a bullet is reduced from $200{\text{ }}m{s^{ - 1}}$to$100{\text{ }}m{s^{ - 1}}$ while travelling through a wooden plank of thickness 10 cm. The retardation, assuming it to be uniform, will be
A) $10\, \times \,{10^4}m/{s^2}$
B) $12\, \times \,{10^4}m/{s^2}$
C) $13.5\, \times {10^4}m/{s^2}$
D) $15\, \times {10^4}m/{s^2}$

Answer 1

Hint
Retardation is nothing but the acceleration of a body in the negative direction. It is defined the same way as acceleration as the rate of change of velocity with respect to time. We need to apply newton’s equations of motion to find the retardation in terms of distance travelled.

Complete step by step answer
According to newton’s equations of motion, we know that:
${v^2}{\text{ }} - {\text{ }}{u^2}{\text{ }} = {\text{ }}2as$
Where, $v$ is the final velocity of the body,
$u$ in the initial velocity of the body,
$a$ is the acceleration of the body,
And $s$ is the distance travelled during this time.
In the question we are given $v$, $u$ and $s$. All we need to find is acceleration of the body is the negative direction.
Substituting the values,
$
\Rightarrow {100^2}{\text{ }} - {\text{ }}{200^2}{\text{ }} = {\text{ }}2a(0.1) \\
\Rightarrow 10000{\text{ }} - {\text{ }}40000{\text{ }} = {\text{ }}0.2a \\
\Rightarrow - \dfrac{{30000}}{{0.2}}{\text{ }} = {\text{ }}a \\
\Rightarrow a\, = \,15\,\times\,{10^4}m/{s^2} \\
$
Therefore, the option with the correct answer is option (D).

Note
One can easily make mistakes in converting the units. In this question we see that the speeds are in meters per second but the thickness is in centimeters. Each equation of motion is defined as the relation between v, u, a, s and t; but taking only 4 at a time. So, if we are given any 3 of these quantities, we can easily find the 4th one by substituting.