A bullet moving at 20 m/sec strikes a wooden plank and penetrates 4cm before coming to stop the time taken to stop is
the average speed while stopping is
... (20 + 0) / 2 = 10 m/s
t = d / r = 4 cm / 10 m/s = .004 s
To determine the time taken for the bullet to stop, we can use the formula for motion with constant acceleration. Here's how you can calculate it:
1. Identify the known values:
- Initial velocity (u) = 20 m/sec
- Displacement (s) = 4 cm = 0.04 m (converted to meters)
- Final velocity (v) = 0 m/sec (as the bullet comes to a stop)
2. Since the bullet comes to a stop, we can assume its acceleration (a) is constant. We need to find this value.
3. Use the equation of motion:
v^2 = u^2 + 2as
4. Rearrange the equation to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Plugging in the known values:
a = (0^2 - 20^2) / (2 * 0.04)
5. Calculate the acceleration:
a = (-400) / (0.08)
a = -5000 m/sec^2 (the negative sign indicates a deceleration)
6. Finally, we can use the formula for velocity with constant acceleration to find the time taken (t):
v = u + at
Plugging in the known values:
0 = 20 + (-5000)t
7. Rearrange the equation to solve for time:
-5000t = -20
t = -20 / -5000
t = 0.004 seconds
Therefore, it takes 0.004 seconds for the bullet to come to a stop after penetrating 4cm into the wooden plank.