12. The speed of a bullet as it travels down the barrel of a rifle toward the op
ID: 1529924 • Letter: 1
Question
12. The speed of a bullet as it travels down the barrel of a rifle toward the opening is given by v = 5.00^7 t^2 + 3.00 × 10^5 t (Look at pic for clarification)
Where v is in meters per square second and t is in seconds. The acceleration of the bullet just as it leaves the barrel is zero.
• Determine the acceleration and position of the bullet as functions of time when the bullet is in the barrel
• Determine the time interval over which the bullet is accelerated
• Find the speed at which the bullet leaves the barrel.
• What is the length of the barrel?
• Can we use the kinematics equation to analyze this problem? Why or Why not?
ize 12. speed of a bullet as it travels down the barrel of a rifle toward the opening is given by The a v 5.00 3.00 x 10 Where v is in meters per square second and t is in seconds. The acceleration of the bullet just as it leaves the barrel is zero. Determine the acceleration and position of the bullet as functions of time when the bulle is in the barrel Determine the time interval over which the bullet is accelerated Find the speed at which the bullet leaves the barrel. What is the length of the barrel? Can we use the kinematics equation to analyze this problem? Why or why not?Explanation / Answer
Ans:-
v=-5*10^7t^2 + 3*10^5t
1]acceleration=dv/dt = 3*10^5 – 10*10^7*t = 3*10^5 – 1*10^8*t
displacement from position at time 0 ,
By taking integration
X= 1.5*10^5*t^2 - 1.667*10^7*t^3
(b) at accel = 0,
3*10^5 – 1*10^8*t = 0,
3*10^5 = 1*10^8*t, t=3*10^5/1*10^8 = 3*10^-3s
the bullet is accelerated for 3 milliseconds
(c) velocity after 3 milliseconds = 3*10^5t – 5*10^7t^2 = 3*10^5*3*10^-3 – 5*10^7*9*10^-6
= 9*10^2 – 45*10^1 = 9*10^2 - 4.5*10^2 = 4.5 *10^2m/s
(d) displacement after 3 milliseconds = 1.5*10^5*t^2 - 1.667*10^7*t^3
= 1.5*10^5*9*10^-6 - 1.667*10^7*27*10^-9 = 13.5*10^-1 – 45*10^-2 = 1.35 - 0.45 = 0.9 meters. the length of the barrel is 90 centimeters
E] no because this is simple and straight forward calculation need not use kinematical equation
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