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The velocity of a particle is
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Vector Mechanics For Engineers
- The flow of an oil is described by the velocity field: v= (3y)êx + (0.6t^2 + 2)êy Where t and y are measured in seconds and meters, respectively, such that the components of the velocities are expressed in m/s. a) If an oil particle was at the origin when t = 0s, determine its position in time t = 2s, and sketch the particle's path in the X-Y plane. b) What are the magnitude and direction of the particle's velocity at said instant of time? c) What are the magnitude and direction of the acceleration of the particle at said instant of time?arrow_forwardQ No 1: The position of a particle moving along the x-axis is given by x=A+B t3, where A=9.75 cm and B=1.50cm/s3.consider the time interval t=2 to t=3s and calculate (a).the average velocity; (b).the instantaneous velocity at t=2s;(c). the instantaneous velocity at t=3s;(d). the instantaneous velocity at t=2.5s;(e). the instantaneous velocity when the particle is midway between its positions at t=2s and t=3s.arrow_forwardThe horizontal motion of the plunger and shaft is arrested by the resistance of the attached disk which moves through the oil bath. The velocity of the plunger is v0 = 3.1 m/s in the position A where x = 0 and t = 0, and the deceleration is proportional to v so that a = -kv where k = 0.32 s-1. Find (a) the velocity when t = 2.9 s, (b) the position x when t = 2.9 s, (c) the velocity when x = 4.2 m.arrow_forward
- A particle is moving along the x-axis and its velocity in m/s is given by: v = t 2 −4t−12. When t = 0 s, the particle’s displacement from the origin is 20 m. determine the particle’s position at t = 6 s.arrow_forwardWhen a particle travels in a uniform circular motion, all the following stay constant excluding: A)Radius B)Acceleration C)Speed D)Velocityarrow_forwardAn airport shuttle train travels between two terminals that are 1.6 mi apart. To maintain passenger comfort, the acceleration of the train is limited to ±4 ft/s2 , and the jerk, or rate of change of acceleration, is limited to ±0.8 ft/s2 per second. If the shuttle has a maximum speed of 20 mi/h, determine (a) the shortest time for the shuttle to travel between the two terminals, (b) the corresponding average velocity of the shuttle.arrow_forward
- Non-uniformly acceleratedmotion& Motion Curves 1.. The brake mechanism used to reduce a gun recoil consists of a piston attached to a barrelmoving in the fixed cylinder filled with oil. As the barrel recoils with an initial velocity v0, the piston moves and the oil is forced through the orifices in the piston, causing the piston and the cylinder todecelerate at a rate proportional to their velocities. Determine v (t), x (t), and v (x)arrow_forwardThe curvilinear motion of a particle is defined by vx = 50− 16t and y = 100 − 4t2, where vx is in meters per second, y is in meters, and t is in seconds. It is also known that x = 0 when t = 0. - Plot the path of the particle. - Determine its velocity and acceleration when the position y = 0 is reached.arrow_forwardThe velocity of a particle traveling along a straight line is v = (3t2 – 6t) ft/sec, where t is inseconds. If s = 4 ft when t = 0, determine the position of the particle when t = 4sec. Whatis the total distance traveled during the time interval t = 0 and t = 4 sec? What is theacceleration when t = 2sec? *Draw the diagramarrow_forward
- 1. In this type of motion, the acceleration “a” of the particle is zero for every value of “t”.2. When a particle P is moving to a position P’ with their corresponding change in radius of curvature and change in the arc length respectively with respect to the origin, the motion is simply define as?3. This component of the particle was shown to be equal to the time derivative of the position coordinate x.arrow_forwardA truck is traveling south at a speed of 70 km/h toward an intersection. A car is traveling east toward the intersection at a speed of 80 km/h. The direction of the car to the truck is estimated asarrow_forwardThe velocity of a particle is v = 200 + 30t 2 + t 4 /2 , where v is in m/s and t is in sec. if the particle is at x = 0 when t = 0. Find the position of particlearrow_forward
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