# Homework Help: Speed of bullet

1. Sep 27, 2004

### UrbanXrisis

The speed of a bullet as it travles down the barrel of a rifle towards the opening is given be the expression v=(-5.0*10^7)t^2 + (3.0*10^5)t, where v is in meters per second and t is in seconds. The acceleration of the bullet just as it leaves the barrel is zero.

(a) determine the acceleration and position of the bullet as a function of time when the bullet is in the barrel.

I multiplied everything by t to get the position equation: x=(-5.0*10^7)t^3 + (3.0*10^5)t^2

I divided everything by t to get the acceleration equation: a=(-5.0*10^7)t + (3.0*10^5)

is this thougth process correct?

(b) determine the length of time the bullet is accelerated.
you dont know the length of the barrel so is this possible?

(c) Find the speed at which the bullet leaves the barrel
based on question b

(d) what is the length of the barrel
based on question b as well

in need of need hits

2. Sep 27, 2004

### Tide

Differentiate to find the acceleration and integrate to find the position.

3. Sep 27, 2004

### UrbanXrisis

what does differentiate mean?

4. Sep 27, 2004

### Tide

Differentiate means finding the derivative. I assumed from the stated problem that you probably have some calculus experience. If not then you may have to resort to graphing and finding the slope of the curve at several points to make a graph of acceleration.

5. Sep 27, 2004

### UrbanXrisis

for question B, I need to find the time, how would I do that?

6. Sep 28, 2004

### Tom McCurdy

$$a= 300000-100000000t$$
$$0=300000-100000000t$$
$$t=3/1000$$

$$x=150000x^2-\frac{50000000x^3}{{3}}$$
$$x=.9 meters$$

7. Sep 28, 2004

### Tide

For that one you have to integrate!

8. Sep 28, 2004

### Tom McCurdy

for the velocity question just plug in when you solved for time

9. Sep 28, 2004

### Tom McCurdy

I just found the derivative of the V for a and integrated V for x

10. Sep 28, 2004

### UrbanXrisis

how do you know acceleration is zero?

11. Sep 28, 2004

### Tom McCurdy

Easy way to find derivitave
take each chuck and do dervitiave of $$cx^n = ncx^{n-1}$$
to integrate
take
$$bx^n = (n+1)x= c/(n+1)x^{n+1}$$

where n is power
c is orignial coeffiecnt
x is variable

12. Sep 28, 2004

### Tom McCurdy

You gave that to me in the problem

13. Sep 28, 2004

### UrbanXrisis

oh, that's right!! So the speed of the bullet would just be m/s.....9m/.003s?

14. Sep 28, 2004

### Tom McCurdy

I just found velocity for it usuing the original equation
you gave me
which gave a velocity of 450 m/s

15. Sep 28, 2004

### UrbanXrisis

wait...all I have to do is sub .003 into the original velocity equation to get 450m.s right?

16. Sep 28, 2004

### UrbanXrisis

17. Sep 28, 2004

### Tom McCurdy

btw the x distance i got was 0.9 meters not 9 meters