My Nates Ask Your ponts SerpSES 2P (2,7 \"es,where v is in meters per second and

Question

My Nates Ask Your ponts SerpSES 2P (2,7 "es,where v is in meters per second and r is i, seconds. The The speed of a tunet asittraveltdown the barrel of a rifle toward the apering i, given by v , (415×10 acceleration of the bullet just as it leaves the barrel is zero (a) Determine the acceleration and position of the bullet as a furction of time when the bullet is o the barrel. (Use t as necessary and round all numerical coefficients to exactly 3 signsificant figures) ) Determine the length of time tve buler is accaherated ) Find the speed at which the butlet leaves the ba d) What is the bength of the barrelr Noed Help? Loo

Explanation / Answer

(a) v = (-4.15*107)t2 + (2.75*103)t
Now we know that acceleration,
a = dv/dt = (-4.15*107)*(2t)+(2.75*103)
a =  (-8.3*107)t+(2.75*103)
We know that
v = dx/dt
dx = vdt
on integration both side
x =  (-4.15*107)(t3/3) + (2.75*103)(t2/2)
x = (-1.383*107)t3 + (1.375*103)t2
(b) When bullet leave the barrel acceleration is zero therefore
a =  (-8.3*107)t+(2.75*103)
putting a = 0
0 =  (-8.3*107)t+(2.75*103)
t = 3.31*10-5 s
(c) Putting the value of t in equation of V
v = (-4.15*107)t2 + (2.75*103)t
v =  (-4.15*107)(3.31*10-5 )2 + (2.75*103)(3.31*10-5 )
v = -45.467*10-3 + 91.02*10-3
v = 45.6*10-3 m/s
(d) x = (-1.383*107)t3 + (1.375*103)t2
x = (-1.383*107)(3.31*10-5)3 + (1.375*103)(3.31*10-5)2
x = -50.15*10-8 + 150.6*10-8
x = 100.45*10-8 m

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