A bullet travelling with velocity 60m/s penerates a trunk and comes to rest covering 0.5m. calculate the time taken during the retardation
average velocity=30m/s
time=distance/avgvelocity=.5m/(30m/s)=1/60 th second
V^2 = Vo^2 + 2a*d = 0,
60^2 + 2a*0.5 = 0,
a = -3600 m/s^2.
V = Vo + a*t = 0,?.
60 + (-3600)t = 0,
t = ?.
To calculate the time taken during the retardation, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, as the bullet comes to rest)
u = initial velocity (60 m/s)
a = acceleration (retardation)
s = displacement (0.5 m)
Since the bullet comes to rest, the final velocity is 0 m/s. Substituting the values into the equation:
0^2 = 60^2 + 2a(0.5)
Simplifying further:
0 = 3600 + a
Rearranging the equation:
a = -3600
The negative sign indicates that the bullet is decelerating or experiencing retardation. Now, we can use another equation of motion to find the time (t) taken.
v = u + at
Since the final velocity is 0 m/s, and the initial velocity is 60 m/s, substituting the values:
0 = 60 + (-3600)t
Rearranging the equation:
3600t = 60
t = 60 / 3600
Simplifying further:
t = 1 / 60
Therefore, the time taken during the retardation is 1/60 seconds.