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The acceleration of a particle is defined by the relation
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- The acceleration of a particle is defined by the relation a= 3e-0.2t, where a and t are expressed in ft/sa2 and seconds, respectively. Knowing that x= 0 and v= 0 at t= 0, determine the velocity and position of the particle when t= 0.5 s.arrow_forwardAssuming a uniform acceleration of 11 ft/s2 and knowing that the speed of a car as it passes A is 30 mi/h, determine (a) the time required for the car to reach B, (b) the speed of the car as it passes B.arrow_forwardBased on experimental observations, the acceleration of a particle is defined by the relation a = –(0.1 + sin x/b), where a and x are expressed in m/s2 and meters, respectively. Know that b = 0.80 m and that v = 1 m/s when x = 0. Determine the position where the velocity is maximum.arrow_forward
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- The acceleration of a particle is defined by the relation a = 3e-0.2t, where a and t are expressed in ft/s2 and seconds, respectively. Knowing that x = 0 and v = 0 at t = 0; Determine the position in feet of the particle when t = 5 s.arrow_forwardThe acceleration of a particle is defined by the relation a = 3e-0.2t, where a and t are expressed in ft/s2 and seconds, respectively. Knowing that x = 0 and v = 0 at t = 0; Determine the velocity in ft/s of the particle when t = 5 s.arrow_forwardThe acceleration of a particle is defined by the relation a = kt^2. Knowing that v = -9 m/s when t = 0 and that v = +9 m/s when t = 3 s, determine the constant k.arrow_forward
- The motion of a particle is defined by the relation v = 4t^2 + 3t – 5. Knowing the displacement S= -2ft when t = 0 sec, determine the displacement and acceleration when t = 3 sec.arrow_forwardTwo highway checkpoints A and B are separated by 12 km. The speed limits for the first 8 km and the last 4 km are 100 km/h and 70 km/h, respectively. Drivers must stop at each checkpoint and the specified time between A and B is 8 min and 20 seconds. Knowing that a car accelerates and decelerates at the same constant value, determine the magnitude of its acceleration if the speed limit is traveled as much as possible.arrow_forward. The motion of a particle is defined by the relation x = 6t^4 – 2t^3 – 12t^2 + 3t + 3, where x and t are expressed in meters and seconds, respectively. Determine the time, the velocity, and the position when a = 15 m/sec^2.arrow_forward
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