A bullet moving at 20m/sec strikes a wooden plank and penetrates 4cm before coming to stop.The time taken to stop is?
To find the time taken for the bullet to stop, we can use the equation of motion:
v = u + at
Where:
v = final velocity (0 m/s, since the bullet comes to a stop)
u = initial velocity (20 m/s)
a = acceleration
t = time taken
Since the bullet comes to a stop, the final velocity is zero (v = 0), and the initial velocity is 20 m/s (u = 20 m/s). We need to find the acceleration (a) and the time taken (t).
To find the acceleration, we can use the equation:
v^2 = u^2 + 2as
Where:
s = displacement (4 cm = 0.04 m)
a = acceleration
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Plugging in the given values, we can calculate the acceleration:
a = (0^2 - 20^2) / (2 * 0.04)
a = -400 / 0.08
a = -5000 m/s^2 (negative sign indicates deceleration)
Now that we have the acceleration, we can use the first equation of motion to find the time taken (t):
v = u + at
0 = 20 + (-5000) * t
Rearranging the equation to solve for t:
-5000t = -20
t = -20 / (-5000)
t = 0.004 seconds
Therefore, the time taken for the bullet to stop is 0.004 seconds.
ave. velocity = (20 + 0) / 2 = 10 m/s
.04 m / 10 m/s = .004 s