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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
- A Based on observations, the speed of a jogger can be approximated by the relation v = 6.4 (1 − 0.03x)0.4 , where v and x are expressed in mi/h and miles, respectively. Knowing that x = 0 at t = 0, determine (a) the distance the jogger has run when t =1.5 h, (b) the jogger’s acceleration in ft/s2 at t = 0, (c) the time required for the jogger to run 5 mi.arrow_forwardEx.5.2 The position of a particle which moves along a straight line is defined by the relation x = t3 - 6t2 -15t + 40, where x is expressed in m and t in sec. Determine (a) the time at which the velocity will be zero, (b) the position and distance traveled by the particle at that time, (c) the acceleration of the particle at that time, d) the distance traveled by the particle from t= 4 s to t = 6 s. %3Darrow_forward6) A ball is thrown vertically upward from the surface of the earth with an initial velocity of 30 m/s. Two seconds later a second ball is thrown upward from the same point with a velocity of 24 m/s. Derive an expression for the relative position, velocity, and acceleration of ball 1 with-respect-to ball 2 for time t≥2sec. (neglect air resistance and assume acceleration of gravity is 9.81 m/s2.arrow_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_forwardAt a certain point in the reentry of the space shuttle into the earth's atmosphere, the total acceleration of the shuttle may be represented by two components. One component is the gravitational acceleration g = 9.67 m/s² at this altitude. The second component equals 10.66 m/s² due to atmospheric resistance and is directed opposite to the velocity. The shuttle is at an altitude of 49.6 km and has reduced its orbital velocity of 28300 km/h to 16160 km/h in the direction = 1.23°. For this instant, calculate the radius of curvature of the path and the rate i at which the speed is changing. Answers: p= i = i i km m/s²arrow_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
- Write the vector expression for the acceleration a of the mass center G of the simple pendulum in both n-t and x-y coordinates for the instant when 8 = 65° if 0 = 2.47 rad/sec and 0 = 3.625 rad/sec². Answers: a = ( i a=i XIII 3.7' mn 8 en + i+ i i et) ft/sec² j) ft/sec²arrow_forwardAt a certain point in the reentry of the space shuttle into the earth's atmosphere, the total acceleration of the shuttle may be represented by two components. One component is the gravitational acceleration g = 9.56 m/s2 at this altitude. The second component equals 11.25 m/s² due to atmospheric resistance and is directed opposite to the velocity. The shuttle is at an altitude of 47.9 km and has reduced its orbital velocity of 28300 km/h to 14750 km/h in the direction = 1.88°. For this instant, calculate the radius of curvature of the path and the rate i at which the speed is changing. Answers: p= i = i FU km m/s²arrow_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
- 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_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_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_forward
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