Question

The velocity of a bullet is reduced from 200 ms^-1 to 100 ms^-1 while travelling through a wooden plank of thickness 10cm. The retardation, assuming it to be uniform, will be 

1) 10 x 10⁴ ms^-2 

2) 12 x 10⁴ ms^-2 

3) 13.5 x 10⁴ ms^-2 

4) 15 x 10⁴ ms^-2

Answer 1

Correct option is 4) 15 x 10⁴ ms^-2

Initial velocity = 200 m/s

Final velocity (v) = 100 m/s

distance s = 10 cm = 0.1 m

Using the relation of equation of motion

\(v^2 = u ^2 + 2 as\)

\(a =\frac {v^2 - u^2}{2s} = \frac {(100)^2 - (200)^2}{2 \times 0.1}\)

\(= \frac {10000-40000}{2\times 0.1} = \frac {-300000}{2}\)

= -150000 m/s²

= -15 x 10⁴ m/s²

(-) minus sign denotes retardation.