Physics 101 mechanics help -- Bullet fired by a rifle barrel

[EishaR]

Homework Statement

A repeating rifle fires 2 LR bullets such that as they travel down the barrel of the rifle their speed is given by v = (−5.00 ✕ 107)t2 + (2.80 ✕ 105)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.
Determine the acceleration (in m/s2) and position (in m) of the bullet as a function of time when the bullet is in the barrel. (Use the following as necessary: t. Round all numerical coefficients to at least three significant figures. Do not include units in your answers. Assume that the position of the bullet at t = 0 is zero.)
a (t)=
x(t)=

(b)Determine the length of time the bullet is accelerated (in s).

(c) Find the speed at which the bullet leaves the barrel (in m/s).

(d) What is the length of the barrel (in m)?

Relevant Equations

y v = (−5.00 ✕ 10^7)t2 + (2.80 ✕ 10^5)t,

a) a= dv/dt = 2(5*10^5)t+2.8*10^5
2(5*10^5)(0)+2.8*10^5=2.8*10^5m/s^2

 

[bob012345]

Homework Statement:: A repeating rifle fires 2 LR bullets such that as they travel down the barrel of the rifle their speed is given by v = (−5.00 ✕ 107)t2 + (2.80 ✕ 105)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.
Determine the acceleration (in m/s2) and position (in m) of the bullet as a function of time when the bullet is in the barrel. (Use the following as necessary: t. Round all numerical coefficients to at least three significant figures. Do not include units in your answers. Assume that the position of the bullet at t = 0 is zero.)
a (t)=
x(t)=

(b)Determine the length of time the bullet is accelerated (in s).

(c) Find the speed at which the bullet leaves the barrel (in m/s).

(d) What is the length of the barrel (in m)?
Relevant Equations:: y v = (−5.00 ✕ 10^7)t2 + (2.80 ✕ 10^5)t,

a) a= dv/dt = 2(5*10^5)t+2.8*10^5
2(5*10^5)(0)+2.8*10^5=2.8*10^5m/s^2

For the first part, check your derivative. You must attempt the other parts also.

 

[haruspex]

How did −5.00 ✕ 10^7 turn into +5.00 ✕ 10^5?