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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_forward2/137 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_forward
- Q2) 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_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_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_forward1. The motion of a particle is defined by the relation x = -10² + 8t + 12, where x and t are expressed in meters and seconds, respectively. Determine the position, the velocity, and the acceleration of the particle when t = 1 s. 2. The vertical motion of mass A is defined by the relation x = 10 sin 2t +15cos2t +100, where x and t are expressed in mm and seconds, respectively. Determine (a) the position, velocity and acceleration of A when t = 1 s, (b) the maximum velocity and acceleration of A. A mall ale: amall boring Paperarrow_forward
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