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The acceleration of a particle is defined by the relation a
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Vector Mechanics For Engineers
- A muzzle-loading rifle fires 22LR bullets such that as they travel down the barrel of the rifle their speed is given by v = (-5.25 x 1o')t? + (2.40 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/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) = m/s2 x(t) = m (b) Determine the length of time the bullet is accelerated (in s). 2.3*10**-3 (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)? marrow_forward3) Two particles, A & B, move along parallel rectilinear paths. At t=0 the particles are directly opposite one another. Particle A moves according to SA = 12t² - 4t³ inches and particle B moves with a constant speed of 12 inches/ second. (a) Determine the relative position of A with respect to B at t = 1 second. (b) Determine the relative velocity of A with respect to B at t = 1 second. ANS. SA/B = -4 inches VA/B = 0 inches/secarrow_forwardt3 – 2t2 + 7 3. The motion of the particle along a straight line is governed by the relation a = where a is the acceleration in m/s² and t is the time in seconds. At time t = A second, the velocity of the particle is v m/s and the displacement is d m. Calculate the displacement, velocity and acceleration at timet = 2 seconds. - A = 1.476 second %3D 14.764 .m/s V = d = 218arrow_forward
- The acceleration of a particle moving horizontally under rectilinear motion is defined by the relation a=9.4t2-4.6t where a is in ft/s2 and t is in s. Initially, the particle is moving at 6ft/s and started at x=9.6 ft. Determine the position of the particle at t=4.4s. Round off only on the final answer expressed in 3 decimals. Indicate appropriate units.arrow_forwardIn a 400-m race, runner A reaches her maximum velocity vA in 4 s with constant acceleration and maintains that velocity until she reaches the halfway point with a split time of 25 s. Runner B reaches her maximum velocity VB in 5 s with constant acceleration and maintains that velocity until she reaches the halfway point with a split time of 25.2 s. Both runners then run the second half of the race with the same constant deceleration of 0.1 m/s2. Determine (a) the race times for both runners, (b) the position of the winner relative to the loser when the winner reaches the finish line.arrow_forwardQ2) The acceleration of a particle as it moves along a straight line is given by a= 2t –1. and v= 2 when t= 0, determine the particle's velocity and position when t=6 s . A determine the total distance the particle travels during this time period.arrow_forward
- 2/137 The curvilinear motion of a particle is governed by the polar coordinates r = t³/3 and 0 = 2 cos (mt/6), wherer is in meters, is in radians, and t is in seconds. Specify the velocity v and acceleration a of the particle when t = 2 s. Ans. v = 4e₁. a = 2.42e, m/s 1.807e, 7.99e, m/s²arrow_forwardThe equation of motion of a particle is s (t) = 2t3-5t2 + 3t + 4, where s is measured in centimeters and t in seconds. Determine the acceleration as a function of time. What is the acceleration after 2 seconds?arrow_forwardThe acceleration of a particle is defined as a 0 (4/3)t. The particle starts at t=0 with v=0. 1 The time when the velocity is again zero. The position and velocity when t=3s Select one: OA 1-3sx(3)- 29.3 m and v(3) = 0 m/s OB. 1-2x(3) 29.3 m and v(3) = 10 m/s Oct-3gx(3) 20.87 m and v(3) = 12.67 m/s OD 1-1sx(3)=9.43 m and v(3) = 8.67 m/s O Aarrow_forward
- 3. a) The velocity of a platform in an amusement park which moves along the s-axis is given by v = 2– 4t + 5t²ª , where t is in seconds and v is in m/s. The platform is at the position S, = 3 'm when =0 Determine: (i) The position S, velocity v, and acceleration a when != 3s. (ii) The time at which the velocity of the platform is maximum. b) The race car A in Figure Q3 follows path a-a while race car B follows path b-b on the unbanked track. If each car has a constant speed limited to that corresponding to a lateral (normal) acceleration of 0.8g, determine the times a and 's for both cars to negotiate the turn as delimited by the line C-C. C a b 88 m 72 m b B a Aarrow_forwardA ball is being thrown vertically upward and being caught at the same elevation (original position) in a total time of 10.26 seconds. The time it takes for the ball to fly up to its maximum height is equal to the time it takes to land from maximum height down to its original position. What is the initial velocity in meters per second that is applied to the ball? Use the value of gravity in 2 decimal places. ↑ t1 t = t2 Use up to 4 decimal places. NOTE: Do not assume that this is the same problem as the previous question. The numerical values for each question are different. 50.3253arrow_forward2 The motion of a particle is defined by the relation. x=t²-10t+30 where, X in meters, t in sec. Determine 1 when the velocity is zero. (5 sec) 2 the position and total distance traveled when t≤ 8 sec (x+=8=14m, Distance = 39 m).arrow_forward
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