A bullet fired horizontally into a thick wooden block undergoes uniform deceleration. It takes 0.1 s to travel through the first 30 cm of the block, and its velocity at the end of this 30 cm is exactly half of its entry velocity. What is the entry velocity of the bullet?

Step-by-step solution

Let the entry velocity of the bullet be u and the final velocity after travelling 30 cm be v . Given: Distance s = 30 cm = 0.3 m Time t = 0.1 s Final velocity v = u 2 For uniformly accelerated (or decelerated) motion, the displacement can be expressed in terms of average velocity: s = ( u + v 2 )t Substituting the given values: 0.3 = ( u + u 2 2 ) 0.1 0.3 = ( 3u 4 ) 0.1 3 = 3u 4 u = 4 m s ⁻¹ The entry velocity of the bullet is 4 m s ⁻¹ . Answer: 4 m s ⁻¹