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- A body moves along a linear path and its rate of change of velocity varies with time and is written as a=2-3t, where t is the time in second. After 5 second, from start of observation its velocity is determined to be 20 m/s. After 10 second from start of observation, the body is at 85 m far from the origin. Determine the following:a. Rate of change of velocity and velocity at the start of motion.b. Distance from the origin at the start of observationc. Time after start of observation in which the velocity becomes zero.arrow_forward5. Tests reveal that a normal driver takes about 0.75 s before he or she can react to a situation to avoid a collision. It takes about 3 s for a driver having 0.1% alcohol in his system to do the same. If such drivers are traveling on a straight road at 30 mph (44 ft/s) and their cars can decelerate at 2 ft/s², determine the shortest stopping distance d for each from the moment they see the pedestrians. Moral: If you must drink, please don't drive! v₁ - 44 ft/sarrow_forwardThe motion of a particle is defined by the function x = at3 - bt2 - ct + d where x is in centimeters and t is in seconds When is the particle at rest if a = 1.3, b = 3.5, c = 8.3, and d = 5.2?arrow_forward
- The motion of a particle is defined by the parametric equations ax =0.8t, ay =2–0.3t, az =5 where “a” is in m/s2 and t in seconds.The particle is at rest and is placed at the origin at t = 0. What is the acceleration of the particle after 10 seconds? What is the velocity of the particle after 10 seconds?arrow_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_forwardA small toy car moves around a circular track with a 1 m radius. It starts at rest, and increases its speed at a constant rate of v = 0.8 m/s². The car will come off of the track when a ≥ 5 m/s². How many revolutions of the track will the car complete before it comes off the track? Enter a decimal number for partial revolutions. revolutionsarrow_forward
- 2/137 The curvilinear motion of a particle is governed by the polar coordinates r = t³/3 and 0 = 2 cos (nt/6), where r 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 = 4e, a = 2.42e, m/s 1.807e, 7.99e, m/s² -arrow_forwardF(t) K: 3. A particle with a mass of 3 kg has velocity = 5î + 7ĵ- 3km/s. The total force acting on the particle is given by F = 3Aî - 2Aĵ + 4Ak N, where A is an unknown constant. Determine the value of A such that the x-component of the particle's velocity is 10 m/s after the force is applied for 2 seconds. Also determine the particle's velocity vector at this time.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_forward
- 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_forwardThe acceleration of a particle traveling along a straight line is a = ¼ s1/2 m/s2 ,where s is in meters. If v = 0 m/s and s = 1 m when t = 0 s, determine the particle’s velocity at s =2 m.NOTE #1 – A sketch of the scenario should be created by you to enhance your work.NOTE #2 – A particle is rather uninspiring, yet they are suitable in learning engineering scienceprinciples. You are welcome to spice up this problem by replacing the particle with a rigid bodyof interest to you. You are welcome to comment on your answer how replacing abstract conceptswith tangible examples influences your learning of dynamics topicsarrow_forwardStarting from x=0 with an initial velocity, a particle is given an acceleration a=0.1(v2 +16)1/2, where a and v are expressed in ft/s2 and ft/s respectively. Determine a) the position of the particle when v=3ft/s, b) the speed and acceleration when x=4 ft.arrow_forward
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