The velocity of a bullet is reduced from $200 ext{ m/s}$ to $100 ext{ m/s}$ while travelling through a woo

Question

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

Accepted Answer

1.  **Identify Given Values:**
    *   Initial velocity, $u = 200 	ext{ m/s}$.
    *   Final velocity, $v = 100 	ext{ m/s}$.
    *   Displacement (thickness), $s = 10 	ext{ cm} = 0.1 	ext{ m}$ (Note: Unit conversion is crucial).
2.  **Select Formula:** Use the kinematic equation relating velocity, acceleration, and displacement: $v^2 = u^2 + 2as$ .
3.  **Calculation:**
    $(100)^2 = (200)^2 + 2a(0.1)$
    $10000 = 40000 + 0.2a$
    $0.2a = 10000 - 40000$
    $0.2a = -30000$
    $a = \frac{-30000}{0.2} = -150000 	ext{ m/s}^2$.
4.  **Scientific Notation:**
    Magnitude of acceleration (retardation) $= 150000 	ext{ m/s}^2 = 15 	imes 10^4 	ext{ m/s}^2$.

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