A bullet is fired onto a wall with a velocity of 50 m/s. If the bullet is at a depth of 10 cm inside the wall, find the retardation produced by the wall.

A bullet is fired into a wall with a velocity of $50\mathit{ m}/s$. If the bullet stops at the depth of $10\mathit{ cm}$ inside the wall, the retardation provided by the wall is $12500\mathit{ m}/s^2$.

Given that, 
Initial velocity $\mathit{u }= 50\mathit{ m}/s$
Final velocity $\mathit{v }= 0\mathit{ m}/s$ 

distance $\mathit{s }= 10\mathit{ cm}$$= 0.1m$ (As $100\mathit{ cm }= 1\mathit{ m}$)
Acceleration, $a$ is unknown,
We know that,

${\mathit{v}}^{\mathbf{2}}\mathbf{-}\mathit{ }{\mathit{u}}^{\mathbf{2}}\mathbf{=}\mathbf{2}\mathit{a}\mathit{s}$
Substituting the values in the above equation, 
$0\mathit{ – }{\left(50\right)}^2= 2 \times \mathit{ a }\times 0.1$
$0.2\mathit{ a }= -2500$
Acceleration, $\mathit{a }= -12500\mathit{ m}/s^2$
Therefore, retardation (r) $= -a$
$\Rightarrow$ $\mathit{r}\mathbf{=}\mathit{ }\mathbf{12500}\mathit{ }\mathit{m}\mathbf{/}{\mathit{s}}^{\mathbf{2}}$