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.