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- A loaded railroad car is rolling at a constant velocity when it couples with a spring and dashpot bumper system. After the coupling, the motion of the car is defined by the relation 4.8 60 sin16 t xe t − = where x and t are expressed in mm and seconds, respectively. Determine the position, the velocity and the acceleration of the railroad car when (a) t = 0, (b) t = 0.3 s.arrow_forwardTo test its performance, an automobile is driven around a circular test track of diameter d. Determine (a) the value of d if when the speed of the automobile is 45 mi/h, the normal component of the acceleration is 11 ft/s2, (b) the speed of the automobile if d = 600 ft and the normal component of the acceleration is measured to be 0.6g.arrow_forwardThe acceleration record shown was obtained for a small airplane traveling along a straight course. Knowing that x= 0 and v= 60 m/s when t= 0, determine (a) the velocity and position of the plane at t= 20 s, (b) its average velocity during the interval 6 s < t< 14 s.arrow_forward
- Based on observations, the speed of a jogger can be approximated by therelation v = 6.4 (1 − 0.03x)0.4 , where v and x are expressed in mi/h and miles,respectively. Knowing that x = 0 at t = 0, determine (a) the distance the jogger hasrun when t =1.5 h, (b) the jogger’s acceleration in ft/s2 at t = 0, (c) the time requiredfor the jogger to run 5 mi. please show every single step in the process thanksarrow_forward6. The speed of a particle moving in a circle with radius 2.0 m increases its speed constantly at a rate of 4.4 m / s2. At an instant when the magnitude of the total acceleration is 6.0 m / s2, what is the velocity of the particle? Answers: a) 3.9 m/s b) 2.9 m/s c) 3.5 m/s d) 3.0 m/s e) 1.4 m/sarrow_forwardDuring a manufacturing process, a conveyor belt starts from rest and travels a total of 1.2 ft before temporarily coming to rest. Knowing that the jerk, or rate of change of acceleration, is limited to ±4.8 ft/s2 per second, determine (a) the shortest time required for the belt to move 1.2 ft, (b) the maximum and average values of the velocity of the belt during that time.arrow_forward
- The mechanism shown below is used in a distribution center to push boxes along a platform and to a loading area. The input link is driven by an electric motor, which, at the instant shown, has a velocity of 25 rad/s and accelerates at a rate of 450 rad/s2. Knowing that the input link has a length of 250 mm, determine the instantaneous acceleration (m/s2) of the end of the input link in the position shown.arrow_forwardThe angular acceleration of a shaft is defined by the relation a= -0.5ω, where a is expressed in rad/s2 and w in rad/s. Knowing that at t= 0 the angular velocity of the shaft is 30 rad/s, determine (a) the number of revolutions the shaft will execute before coming to rest, (b) the time required for the shaft to come to rest, (c) the time required for the angular velocity of the shaft to reduce to 2 percent of its initial value.arrow_forwardA motorist starts from rest at point A on a circular entrance ramp when t=0, increases the speed of her automobile at a constant rate and enters the highway at point B. Knowing that her speed continues to increase at the same rate until it reaches 69.06 mph at point C, determine themagnitude of the tangential acceleration (ft/s2) from A to B. Round off only on the final answer expressed in 3 decimal places.arrow_forward
- The rotation of the rod OA around O is defined by the relation θ = (3/π)(sen πt), where θ and t are expressed in radians and seconds, respectively. Collar B slides along the rod so that its distance from O is r = 6(1- e-2t ) ,where r and t are expressed in inches and seconds, respectively. When t = 1s determine,a) the velocity of the collar b) the acceleration of the collar, c) the acceleration of the collar relative to the rodarrow_forwardA particle moves in a straight line with a constant acceleration of 1.64 m/s2for 6s, zero acceleration for the next 5s, and a constant decceleration of 1.07 m/s2for 4s. Knowing that the particle starts from the origin and that its velocity is 18 m/s during the zero acceleration time interval . Determine the velocity (m/s) of the particle at t = 4.1 seconds. Round off only on the final answer expressed in three decimal places. PLEASE SHOW YOUR CORRECT AND COMPLETE SOLUTION. ASAP! Thank you.arrow_forwardTo study the performance of a race car, a high-speed camera is positioned at point A. The camera is mounted on a mechanism which permits it to record the motion of the car as the car travels on straightaway BC. It took 0.5 s for the car to travel from the position θ = 60° to the position θ = 35°. Knowing that b = 24 m, determine the average speed of the car during the 0.5-s interval. The average speed of the car during the 0.5-s interval is ______ km/h.arrow_forward
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