A revolving rifle fires 9 mm bullets such that as they travel down the barrel of the rifle their speed is given by v = (-4.85 x 10')² + (2.55 x 10)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 (in m/s) 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) = The acceleration may be determined from the velocity by taking the first derivative of the velocity with respect to time -m/s² %3D x(t) = m (b) Determine the length of time the bullet is accelerated (in s). In the previous step, we determined an expression for the acceleration as a function of time. We have been informed that the bullet's acceleration drops to zero at the end of the barrel. If we set the acceleration (in the expression for the acceleration as a function of time) equal to zero and solving for the time, this time will be the length of time for the bullet to travel the length of the rifle barrel. s (c) Find the speed at which the bullet leaves the barrel (in m/s). m/s (d) What is the length of the barrel (in m)? We have determined an expressn for the position of the bullet (in the rifle barrel) as a function of time [part(a)). We have determined the length of time it takes the bullet to travel the length of the barrel. Entering this time into the expression for the position of the bullet at any time, we can obtain the length of the barrel, m
A revolving rifle fires 9 mm bullets such that as they travel down the barrel of the rifle their speed is given by v = (-4.85 x 10')² + (2.55 x 10)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 (in m/s) 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) = The acceleration may be determined from the velocity by taking the first derivative of the velocity with respect to time -m/s² %3D x(t) = m (b) Determine the length of time the bullet is accelerated (in s). In the previous step, we determined an expression for the acceleration as a function of time. We have been informed that the bullet's acceleration drops to zero at the end of the barrel. If we set the acceleration (in the expression for the acceleration as a function of time) equal to zero and solving for the time, this time will be the length of time for the bullet to travel the length of the rifle barrel. s (c) Find the speed at which the bullet leaves the barrel (in m/s). m/s (d) What is the length of the barrel (in m)? We have determined an expressn for the position of the bullet (in the rifle barrel) as a function of time [part(a)). We have determined the length of time it takes the bullet to travel the length of the barrel. Entering this time into the expression for the position of the bullet at any time, we can obtain the length of the barrel, m
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![A revolving rifle fires 9 mm bullets such that as they travel down the barrel of the rifle their speed is given by
\[ v = (-4.85 \times 10^7)t^2 + (2.55 \times 10^5)t, \]
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 (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.)
\[ a(t) = \quad \underline{\hspace{3cm}} \]
\[ x(t) = \quad \underline{\hspace{3cm}} \, \text{m} \]
The acceleration may be determined from the velocity by taking the first derivative of the velocity with respect to time
\[ \left( a = \frac{dv}{dt} \right) \, \text{m/s}^2 \]
(b) Determine the length of time the bullet is accelerated (in s).
\[ \underline{\hspace{5cm}} \]
In the previous step, we determined an expression for the acceleration as a function of time. We have been informed that the bullet's acceleration drops to zero at the end of the barrel. If we set the acceleration (in the expression for the acceleration as a function of time) equal to zero and solve for the time, this time will be the length of time for the bullet to travel the length of the rifle barrel.
(c) Find the speed at which the bullet leaves the barrel (in m/s).
\[ \underline{\hspace{3cm}} \, \text{m/s} \]
(d) What is the length of the barrel (in m)?
\[ \underline{\hspace{3cm}} \]
We have determined an expression for the position of the bullet (in the rifle barrel) as a function of time [part (a)]. We have determined the length of time it takes the bullet to travel the length of the barrel. Entering this time into the expression for the position of the bullet at any time, we can](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F956b0b66-64e4-41f4-a71b-5dd0228fcfde%2Fa3361259-7354-474a-89ff-43fa7e88d445%2Fgqlejyi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A revolving rifle fires 9 mm bullets such that as they travel down the barrel of the rifle their speed is given by
\[ v = (-4.85 \times 10^7)t^2 + (2.55 \times 10^5)t, \]
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 (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.)
\[ a(t) = \quad \underline{\hspace{3cm}} \]
\[ x(t) = \quad \underline{\hspace{3cm}} \, \text{m} \]
The acceleration may be determined from the velocity by taking the first derivative of the velocity with respect to time
\[ \left( a = \frac{dv}{dt} \right) \, \text{m/s}^2 \]
(b) Determine the length of time the bullet is accelerated (in s).
\[ \underline{\hspace{5cm}} \]
In the previous step, we determined an expression for the acceleration as a function of time. We have been informed that the bullet's acceleration drops to zero at the end of the barrel. If we set the acceleration (in the expression for the acceleration as a function of time) equal to zero and solve for the time, this time will be the length of time for the bullet to travel the length of the rifle barrel.
(c) Find the speed at which the bullet leaves the barrel (in m/s).
\[ \underline{\hspace{3cm}} \, \text{m/s} \]
(d) What is the length of the barrel (in m)?
\[ \underline{\hspace{3cm}} \]
We have determined an expression for the position of the bullet (in the rifle barrel) as a function of time [part (a)]. We have determined the length of time it takes the bullet to travel the length of the barrel. Entering this time into the expression for the position of the bullet at any time, we can
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