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The motion of a particle is defined by the equations
Fig. P11.91
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VECTOR MECH. FOR EGR: STATS & DYNAM (LL
- The rectangular coordinates of a particle which moves with curvilinear motion are given by x = 9.75t + 1.25t²-0.60t3 and y=6.12 + 10.89t-2.01t², where x and y are in millimeters and the time t is in seconds, beginning from t= 0 Determine the velocity v and acceleration of the particle when t-7s. Also, determine the first time that the welocity of the particle makes an angle of 27" with the positive-anis V= 13 25 i i [ mmsarrow_forwardAn airplane takes off as shown following a trajectory described by equation y= kx², where K = 2 × 10-4 ft-1. When x= 1050 ft, the speed of the plane is vo = 110 mph. Using the component system shown, provide the expression for the velocity of the airplane when x = 1050 ft. Express your answer in ft/s. (Round the final answers to four decimal places.) y Ĵ path of A- ·X The expression for the velocity of the airplane is || = < + ^ j) ft/s.arrow_forwardParvinbhaiarrow_forward
- Dynamics of Rigid Bodies - Mechanical Engineering The velocity of a particle moving in the x-y plane is given by (6.91i + 7.17j) m/s at time t = 5.61 s. Its average acceleration during the next 0.017 s is (2.7i + 4.3j) m/s^2. Determine the velocity v of the particle at t = 5.627 s and the angle O between the average-acceleration vector and the velocity vector at t = 5.627 s. Subject: Mechanical Engineeringarrow_forward3. 2) At this instant, car A travels along a straight path while car B travels along a circular path, and the directions of their velocities are shown in the image below. Car A travels with speed va = 23 m/s, which is decreasing at 5 m/s2, car B travels with speed vg = 13 m/s, which is increasing at 4 m/s?. The dimensions r= 250 m and d = 180 m. Determine the magnitude of the relative acceleration (in m/s2 ) of car A with respect to car B. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. VB 4 m/s? CO В VA A | 5 m/s?arrow_forwardQ1: Coal is discharged from the tailgate A of a dump truck with an initial velocity VA= 2 m/s. Determine the radius of curvature of the trajectory described by the coal (a) at Point A, (b) at the point of the trajectory 1 m below Point A. 00 50°arrow_forward
- แสดงวิธีทำให้ดูหน่อยครับarrow_forwardแสดงวิธีทำให้ดูหน่อยarrow_forwardA A particle is moving along a curve. Its x position is described by x = t² m while its y position is given by the function y = 2 + t4 m. Determine the following: a. Sketch an x-y plot of the particle's path, showing the starting position (at t = 0) of and the direction taken by the particle b. At t= 1 sec, determine the velocity and acceleration vectors of the particle. (Express in Cartesian vector form) c. At t = 1 sec, determine the normal and tangential components of the acceleration. Show the vector diagram of the components. d. Determine the magnitude of the acceleration at t = 1 sec.arrow_forward
- A particle travels to the right along a straight line with a velocity v = [5/(4+s)]m/s where s is in meters. Determine its position when t = 6 s if s = 5 m when t = 0.arrow_forwardAt the instant shown in (Figure 1), the car at A is traveling at 10 m/s around the curve while increasing its speed at 5.5 m/s². The car at B is traveling at 22.5 m/s along the straightaway and increasing its speed at 2 m/s². Figure 100 m 100 m 45° [45° < 1 of 1 VA = 10 m/s Part A Determine the magnitude of the relative velocity of A with respect to B at this instant. Express your answer to three significant figures and include the appropriate units. ► View Available Hint(s) "A/B = Submit Part B 0= Submit Value Part C ^ IVE ΑΣΦ Determine the direction angle of the relative velocity with respect to B at this instant, measured counterclockwise from the positive z axis. Express your answer in degrees using three significant figures. ► View Available Hint(s) C I vec Units ? ↑ Review ?arrow_forward3(a) The velocity of a particle moving in the x-y plane is given by (3.95i + 5.32j) m/s at time t = 5.84 s. Its average acceleration during the next 0.030 s is (4.4i + 3.9j) m/s2. Determine the velocity v of the particle at t = 5.870 s and the angle θ between the average-acceleration vector and the velocity vector at t = 5.870 s.arrow_forward
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