Question

A bullet leaves a rifle with a muzzle velocity of 600 m/s. While accelerating through the barrel of the rifle, the bullet moves a distance of 0.8 m. Determine the acceleration of the bullet (assume a uniform acceleration).​

Answer 1

$\underline \bold{Answer}$

Initial velocity of bullet (u) = 0

Final velocity of bullet (v) = 600m/s

Distance covered by bullet (s) = 0.8 m

We need to find Acceleration of the bullet (a) = ?

Using third equation of Motion

${v}^{2} - {u}^{2} = 2as$

$( {600)}^{2} - (0)^{2} = 2a \times 0.8$

$(360000) - (0) = 2a \times 0.8$

$\large{a = \frac{360000}{2 \times 0.8}}$

$\large{a = \frac{360000}{1.6}}$

⇒ 225,000

Therefore, The acceleration of the bullet is 225,000 m/s^2

★ Equation of Motion give relation between velocity, acceleration, distance covered, time taken for a body in uniform acceleration.

First equation of Motion :- v = u + at

Second equation of Motion :- s = ut + 1/2at^2

Third equation of Motion :- v^2 - u^2 = 2as

★ Unifrom acceleration :- when a body travels in straight line and it's velocity changes by equal amounts in equal intervals of time.

Answer 2

Solution :-

Initial velocity of the bullet ( U ) = 0

Final velocity of the bullet = Muzzle Velocity = V = 600 m/s

Distance travelled to acquire the Muzzle Velocity = S = 0.8 m

To find out the Acceleration, We Will use the Equation,

V² = U² + 2aS

As U = 0, the equation becomes: V² = 2aS

Which gives acceleration,

a = V² / (2S)

= 600² / (2 x 0.8)

= 225000 m/s²