A muzzle-loading rifle fires 22LR bullets such that as they travel down the barrel of the rifle their speed is given by v = (-4.50 x 1o7)t² + (2.75 x 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. (a) Determine the acceleration (in m/s³) 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 : - o is zero.) a(t) = m/s2 x(t) = (b) Determine the length of time the bullet is accelerated (in s). (e) 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)?

The acceleration of an object (in m/s2) is given by the function a(t)=7sin(t)a(t)=7sin(t). The initial velocity of the object is v(0)=−1v(0)=-1 m/s. Round your answers to four decimal places. v(t) = -7cos(t) + 6 The objects displacement from time 0 to 3 is:   17.01216 meters Find the total distance traveled by the object from time 0 to time 3.

An object's position as a function of time in one dimension is given by the expression; 3.89t2 + 2.22t + 7.48 where are constants have proper SI Units. What is the object's average velocity between the times t = 3.16 s and t = 8.38 s?

An object is travelling in 1-dimension (i.e. along the x- axis) with a velocity described by the equation: v(t)=v0+1/6st^3 , where s and v0 are constants. The object’s position, and acceleration at time t = 0 are given by d0, and a0 respectively. In terms of the variables given, what is the average acceleration of the object over the interval from 0 to 2 seconds.

The speed of propagation of the action potential (an electric signal) in a nerve cell depends (inversely) on the diameter of the axon(nerve fiber). If the nerve cell connecting the spinal cord to your feet is 0.9 m long and the nerve impulse is 16 m/s. How long (in s) does it take for the nerve signal to travel this distance ?

A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by  x = 17.2t  and  y = 4.16t − 4.90t2,  where x and y are in meters and t is in seconds. (a) Write a vector expression for the ball's position as a function of time, using the unit vectors î and ĵ. (Give the answer in terms of t.) =         m By taking derivatives, do the following. (Give the answers in terms of t.) (b) obtain the expression for the velocity vector  as a function of time =          m/s(c) obtain the expression for the acceleration vector  as a function of time =          m/s2(d) Next use unit-vector notation to write expressions for the position, the velocity, and the acceleration of the golf ball at t = 3.18 s.   =         m   =         m/s   =         m/s2

An object's position as a function of time in one dimension is given by the expression; 3.89t2 + 2.22t + 7.48 where are constants have proper SI Units. What is the object's average velocity between the times t = 3.16 s and t = 8.38 s? with everything in 3 sig figs

The velocity of an object is given by, = u + at V ds dt. where, u is the initial velocity, a is the acceleration, and ₺ is the time in seconds. Solve the differential equation to obtain the displacement, s, given that at t = 0, s = 7 (metres) : 1 if u = 3 ms ¹, a = 2.4 ms 2, calculate the displacements at t = 4.9 seconds. Give your answer to 2 decimal places.

The position of an object in circular motion is modeled by the given parametric equations, where t is measured in seconds. x=7sin((pi/8)t), y=-7cos((pi/8)t) How long (in sec) does it take to complete one revolution?

According to Los Angeles Air Traffic Control, an Air Force SR-71 has a constant velocity of 1942 knots (999 m/s) along the negative y direction, and a Navy F-18 has an acceleration of 4 m/s^2 along the positive x direction (both of these are fighter jets). What is the acceleration of the F-18 as measured by an observer in the SR-71 (in m/s^2)? [i and j represent unit vectors along the x and y directions respectively]