A bullet moves with a velocity of [tex][tex]$100 \, \text{m/s}$[/tex][/tex] and comes to rest after entering a tree for [tex]0.2 \, \text{m}[/tex]. What is its average velocity?



Answer :

To calculate the average velocity of the bullet as it penetrates the tree, we need to use the concept of average velocity in uniform motion. Here is a step-by-step solution:

1. Identify the initial velocity (u):
The initial velocity of the bullet is given as [tex]\( u = 100 \, \text{m/s} \)[/tex].

2. Identify the final velocity (v):
The final velocity of the bullet, after it comes to rest inside the tree, is [tex]\( v = 0 \, \text{m/s} \)[/tex] since the bullet comes to a stop.

3. Calculate the average velocity (v_avg):
The formula for average velocity when considering uniform acceleration is given by:
[tex]\[ v_{\text{avg}} = \frac{u + v}{2} \][/tex]
Plugging in the values:
[tex]\[ v_{\text{avg}} = \frac{100 + 0}{2} \][/tex]

4. Perform the calculation:
[tex]\[ v_{\text{avg}} = \frac{100}{2} = 50 \, \text{m/s} \][/tex]

Therefore, the average velocity of the bullet as it penetrates the tree is [tex]\( 50 \, \text{m/s} \)[/tex].