# Average Acceleration Question

1. Aug 21, 2012

### DrDonaldDuck

1. The problem statement, all variables and given/known data
"A bullet is fired through a 5.0 cm thick board of some material. The bullet strikes the board with a speed of 200 m/s, and emerges out the other end at 100 m/s.

2. Relevant equations
a= (change in velocity)/(change in time)
average velocity = .5(initial v + final v)

3. The attempt at a solution

a= (-100 m/s)/(.000333 seconds) = -300300 m/s^2
I found .000333s as the time it took for the bullet to pass through the board, using the average velocity of 150 m/s.

Is this correct?

SOLVED.

Last edited: Aug 21, 2012
2. Aug 22, 2012

### Simon Bridge

It helps, if you are unsure of your reasoning, to relate what you did with some other representation... eg. from your equations:

ave speed = distance over change in time:$$\frac{d}{T} = \frac{1}{2}(v + u) \Rightarrow 2d = (v + u)T$$... using distace d, change in time T, final velocity v, initial velocity u.

acceleration is change in speed over change in time:$$a = \frac{v - u}{T} \Rightarrow v = aT + u$$

Soooo... combining them:$$2d = \big ( (aT + u) + u\big )T = aT^2 +2uT \Rightarrow d = uT + \frac{1}{2}aT^2$$... which you will recognize as a kinematic equation.
... so what you've done is basically the same as assuming a constant acceleration, and is consistent with other physics you know.