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Based on observations, the speed of a jogger can be approximated by the relation
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Vector Mechanics for Engineers: Dynamics
- Problem (2): A The acceleration of point A is defined by the relation a = -1.8 sin(kx), where a and x are expressed in m/s² and meters, respectively, and k = 3 rad/m. Knowing that x = 0 and v = 0.6 m/s when t = 0, determine the following: (a) The symbolic equation of the velocity. (b) Position of point A when v = 0. C В Darrow_forwardmoments = 0) in order to determine a force or moment requires a complete free body diagram. Absence of a free body diagram may result in a grade of 'O' for the problem. %3D 1. The acceleration of a particle is directly proportional to time, t, i.e., a = at where a is a constant. At t = 0 s, the position of the particle is -150 mm. Knowing that v = 200 mm/s and x = 75 mm whent = 3 s, determine the position and velocity when t = 5 s.arrow_forwardThe acceleration of a particle moving along the x-axis is given by the relation a = kt m/s?., where k is a constant, and i is in seconds. Supposed that v = -10 m/s, x = x, when / = 0 and x = 0, v = 0 when t = 6 s, determine (a) the value of the constants k and x,, (b) the position as a function of t. %3Darrow_forward
- Jack run on a marathon with a speed that can be approximated by the relation v= 6.5(1.2 - 0.05x) ^ 0.3, where v and x are expressed in mi/h and miles respectively. Knowing that x= 0 at t = 0, determine (a.) the distance Jack has run when t =1h, (b) Jack's acceleration in ft/s^2 at t=0, (c.) the time required for him to run 6 mi. helppparrow_forwardStarting from rest, a bicyclist travels around a horizontal circular path, p= 10 m, at a speed of (0.09t2 + 0.1t) m/s, where t is in seconds. Part A Determine the magnitude of his velocity when he has traveled s = 3 m. Express your answer to three significant figures and include the appropriate units. HA ? Value Units v = Submit Request Answer Part B Determine the magnitude of his acceleration when he has traveled s = 3 m. Express your answer to three significant figures and include the appropriate units. HẢ Value Units a = Submit Request Answerarrow_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_forward
- 1) Some civil engineers are designing an Autobahn connecting Reno and Vegas to reduce the drive time. There are several hilly stretches between the two cities. They would like to keep the magnitude of acceleration on the drivers to be less than one g. They run a test where the speed of a biker decreased uniformly with time from 150 km/h at A to 100 km/h at B over 10 seconds. The radius of curvature for dip A is 200 m. If the magnitude of the total acceleration of the center of the mass of the bike is the same at B as at A, compute the radius of curvature rs of the hill in the road at B. The center of the mass of the car is 0.5 m from the road. [Ans. To Check: re-88.5m] TA = 200 m A VA= 150 km/h H = 0.5 m B VB = 100 km/h TB = ? marrow_forwardA particle moves along a straight line such that its position is defined by s = (t2 – 6t +5) m Part B Determine the average speed of the particle whent = 5.9 s. Express your answer to three significant figures and include the appropriate units. HA ? (Vsp)avg = Value Units Submit Request Answer Part C Determine the acceleration of the particle when t = 5.9 s. Express your answer to three significant figures and include the appropriate units. HA ? Value Units a =arrow_forwarde V:.. | %A£ ]n. Time left 0:19:30 Automobile A and B are initially 30 m apart travelling in adjacent highway lanes at speeds VA = 14.4 km/hr., VB = 23.4 km/hr. at t = 0.0. Knowing that automobile A has a constant acceleration of 0.8 m/s2 and automobile B has a constant deceleration of 0.4 m/s2. The speed of B when it is overtaken by A is: A Side view 73.579 m/s 34.621 m/s 11.564 m/s 2.718 m/s 43.578 m/s IIarrow_forward
- An automobile travels along a straight road at 15.65 m/s through a 11.18 m/s speed zone. A police car observed the automobile. At the instant that the two vehicles are abreast of each other, the police car starts to pursue the automobile at a constant acceleration of 1.96 m/s . The motorist noticed the police car in his rearview mirror 12 s after the police car started the pursuit and applied his brakes and decelerates at 3.05 m/s . (Hint: The police will not go against the law.) a) Find the total time required for the police car to overtake the automobile. b) Find the total distance travelled by the police car while overtaking the automobile. c) Find the speed of the police car a the time it overtakes the automobile. d) Find the speed of theautomobile at the time it was overtaken by the police car.arrow_forwardX Incorrect Car A rounds a curve of 172-m radius at a constant speed of 37 km/h. At the instant represented, car B is moving at 97 km/h but is slowing down at the rate of 2.5 m/s². Determine the velocity and acceleration of car A as observed from car B. A 172 m 10.278 j) m/s 1.885 j) m/s² Answer: VA/B = aA/B = -26.94 0.164 (E) B i + i i + iarrow_forward3. a) The velocity of a platform in an amusement park which moves along the s-axis is given by v = 2– 4t + 5t²ª , where t is in seconds and v is in m/s. The platform is at the position S, = 3 'm when =0 Determine: (i) The position S, velocity v, and acceleration a when != 3s. (ii) The time at which the velocity of the platform is maximum. b) The race car A in Figure Q3 follows path a-a while race car B follows path b-b on the unbanked track. If each car has a constant speed limited to that corresponding to a lateral (normal) acceleration of 0.8g, determine the times a and 's for both cars to negotiate the turn as delimited by the line C-C. C a b 88 m 72 m b B a Aarrow_forward
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