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A bullet travelling with a velocity of 16m/s penetrates a tree trunk and come to rest in 0.4m.find the time taken during the retardation?
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A bullet travelling with a velocity of 16m/s penetrates a tree trunk a...
Calculation of Time Taken during Retardation of Bullet


Given Data:


  • Initial velocity of the bullet, u = 16 m/s

  • Distance travelled by the bullet while stopping, s = 0.4 m

  • Final velocity of the bullet, v = 0 m/s (bullet comes to rest)



Formula:

The formula to calculate the time taken during retardation of the bullet is:

v = u + at

Where,

  • u = initial velocity of the bullet

  • v = final velocity of the bullet

  • a = acceleration of the bullet

  • t = time taken by the bullet to come to rest



We know that the bullet comes to rest after covering a distance of 0.4 m. Hence, we can use the equation of motion to calculate the acceleration of the bullet.

Equation of Motion:

The equation of motion for a body under retardation is:

v^2 = u^2 - 2as

Where,

  • u = initial velocity of the bullet

  • v = final velocity of the bullet

  • a = acceleration of the bullet

  • s = distance travelled by the bullet



Calculation:

Substituting the given values in the equation of motion, we get:

0^2 = 16^2 - 2a(0.4)

Simplifying the above equation, we get:

a = 128 m/s^2

Now, using the formula v = u + at, we can calculate the time taken by the bullet to come to rest:

0 = 16 + (128)t

Simplifying the above equation, we get:

t = 0.125 s

Answer:

Therefore, the time taken during the retardation of the bullet is 0.125 seconds.
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