The velocity of a bullet is reduced from 200m/s to 100m/s while travelling through a wooden block of thickness 10 cm. The retardation, assuming it to be uniform, will be

The correct option is 15x10⁴ m/s².

Understanding the Given Information:
We are given the following values for the bullet traversing the wooden block:
- Initial velocity of the bullet, $u=200\text{m/s}$
- Final velocity of the bullet, $v=100\text{m/s}$
- Thickness of the block (distance travelled), $s=10\text{cm}$

First, we need to convert the distance from centimeters to meters to maintain unit consistency in the SI system:
$s=10\text{cm}=\frac{10}{100}\text{m}=0.1\text{m}$

Formula:
We can use the third equation of motion, which relates initial velocity, final velocity, acceleration, and displacement:
$v^2=u^2+2as$

Here, $a$ represents the uniform acceleration of the bullet.

Step-by-step Calculation:
Substituting the values into the formula:
$(100{)}^2=(200{)}^2+2·a·(0.1)$

Simplifying the calculations:
$10000=40000+0.2a$

Subtracting 40000 from both sides to isolate the acceleration term:
$10000-40000=0.2a$
$-30000=0.2a$

Solving for $a$:
$a=\frac{-30000}{0.2}$
$a=-150000{\text{m/s}}^2$

Expressing this in scientific notation:
$a=-15\times {10}^4{\text{m/s}}^2$

The negative sign represents deceleration or retardation. Thus, the uniform retardation is:
$\text{Retardation}=15\times {10}^4{\text{m/s}}^2$