Exam 1. City Tech, Spring 2017. Problems 6,7,8,9,10

11. The motion of some object is described by the two equations
x = 17.7m∙ cos(t/5s),
y = 17.7m∙ sin(t/5s),
z = 0.
What is the magnitude of the acceleration of this object for the time t=3 s?

12. Let two special objects with equivalent masses attract each other by gravity attraction with the force of 5N. What will be gravity attraction of this two objects if mass of one object is increased 2 times, mass another object is increased 18 times, and the distance between objects is increased 6 times?

13. The maximum speed with which a 1200-kg car can round a turn of radius 80 m on an iced float road without slipping is 32.2 km/h. Find the static friction coefficient between tires and road. Use g=10 m/s².

14. What is maximum possible magnitude of the acceleration of the box shown in the picture? The coefficient of the kinetic friction between the box and the inclined surface is 0.1, the inclined surface angle is 30 degrees, the mass of the box is 10 kg. The inclined surface can not move.







15. Two cars start moving simultaneously from opposite ends of a road. If cars are moving with the equal constant speeds, cars meet each other after the time t₁ from the moment of the start. Find the meeting time if the speed of one car would be twice greater but the speed of another car would be twice less.

16. The velocity of a linear motion is given as a function of the x coordinate: v(x)=C/x, where C is the given constant. Find elapsed time to the motion from the known initial position x₀ to the known final position x₁.