Question

A bullet is moving at a speed of 367 m/s when it embeds into a wall of clay. The bullet penetrates for a distance of 0.0621 m before coming to a stop. Determine the acceleration of the bullet while moving into the clay.

Answer 1

Given :-

Initial velocity of bullet = 367 m/s

Distance traveled by bullet = 0.0621 m

To Find :-

The acceleration of the bullet while moving into the clay.

Analysis :-

Here, we are given with the distance and initial velocity of the bullet.

Substitute the given values using the third equation of motion and find the acceleration accordingly.

Solution :-

We know that,

• u = Initial velocity
• s = Distance
• a = Acceleration
• v = Final velocity

Using the formula,

$\underline{\boxed{\sf Third \ equation \ of \ motion = v^2 = u^2 + 2as}}$

Given that,

Initial velocity (u) = 367 m/s

Final velocity (v) = 0 m/s

Distance (s) = 0.0621 m

Substituting their values,

(0)² = (367)² + 2a × (0.0621)

0 = 134689 + 2a × (0.0621)

a = -1.08 × 10⁻⁶ m/s²

Therefore, the retardation of the bullet while moving into the clay is -1.08 × 10⁻⁶ m/s².