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Vector Mechanics For Engineers
- Three seconds after automobile B passes through the intersection shown in figure for Q. No. 3, automobile A passes through the same intersection. Knowing that the speed of each automobile is constant, determine (a) the relative velocity of B with respect to A, (b) the change in position of B with respect to A during a 4-s interval, (c) the distance between the two automobiles 2s after A has passed through the intersection. Very urgent sir, please solve ASAP.arrow_forwardA 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_forwardA girl operates a radio-controlled model car in a vacant parking lot. The girl’s position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the x-y plane. She drives the car in a straight line so that the x coordinate is defined by the relation x(t) = 0.5t3 - 3t2 + 3t2 + 3t + 2, where x and t are expressed in meters and seconds, respectively. Determine (a) when the velocity is zero, (b) the position and total distance travelled when the acceleration is zero.arrow_forward
- 6. 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_forward7. Two cars are traveling around identical circular circuits. A car A travels at a constant speed of 20 m / s. Car B starts at rest and accelerates with constant tangential acceleration until its speed is 40 m / s. When car B has the same (tangential) speed as car A, it is always true that: choose an asnwer A-)it is passed to car A. B-)which has the same linear (tangential) acceleration as car A. C-)which has the same centripetal acceleration as car A. D-)which has the same total acceleration as car A .. E-)which has traveled further than the car A from the start.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_forward
- The motion of a vibrating particle is defined by the position vector r= 10(1 – e-3t)i + (4e-2t sin 15t)j, where r and t are expressed in millimeters and seconds, respectively. Determine the velocity and acceleration when (a) t= 0, (b) t = 0.5 s.arrow_forwardExperimental data indicate that in a region downstream of a given louvered supply vent the velocity of the emitted air is defined by v = 0.18 v0/x, where v and x are expressed in m/s and meters, respectively, and v0 is the initial discharge velocity of the air. For v0 = 3.6 m/s, determine (a) the acceleration of the air at x= 2 m, (b) the time required for the air to flow from x= 1 to x= 3 m.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 5.2 m/s^2. The car at B is traveling at 24.5 m/s along the straightaway and increasing its speed at 2 m/s^2. 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. Part B: Determine the direction angle of the relative velocity with respect to B at this instant, measured counterclockwise from the positive x axis. Express your answer in degrees to three significant figures Part C: Determine the magnitude of the relative acceleration of A with respect to B at this instant. Express your answer to three significant figures and include the appropriate units. Part D: Determine the direction angle of the relative acceleration with respect to B at this instant, measured counterclockwise from the positive x axis. Express your answer in…arrow_forward
- A particle is moving along a circular path having a radius of 6 in. such that its position as a function of time is given by theta = sin 3t, where theta and the argument for the sine are in radians, and t is in seconds. Determine the magnitude of the acceleration of the particle at theta = 30. The particle starts from rest at u = 0.arrow_forwardA 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 x = 60e - 4.8t sin 16t, where x and t are expressed in millimeters 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_forwardThe damped motion of a vibrating particle is defined by the position vector r =x1[1 - 1/(t+ 1)]i+ (y1e-πt/2 cos 2π)j where t is expressed in seconds. For x1 = 30 mm and y1 = 20 mm, determine the position, the velocity, and the acceleration of the particle when (a) t= 0, (b) t=t 1.5 s.arrow_forward
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