A record is played by spinning the record so that a circular groove in the vinyl slides under the stylus. Suppose that a record turns at a rate of 33 1/3 rev. min, the groove being played is at a radius of 10.0 cm and the bumps in the grove are uniformly separated by 1.75 mm. At what rate (hits per second) do the bumps hit the stylus? Enter units as hertz (Hz). You will need v=rω ω is in rad/s and 1rev = 2 pi rad.

A record is played by spinning the record so that a circular groove in the vinyl slides under the stylus. Suppose that a record turns at a rate of 33 1/3 rev. min, the groove being played is at a radius of 10.0 cm and the bumps in the grove are uniformly separated by 1.75 mm. At what rate (hits per second) do the bumps hit the stylus? Enter units as hertz (Hz). You will need v=rω ω is in rad/s and 1rev = 2 pi rad.

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3. Th valve of an oil carrying duct shown in the Figure is being closed such that the oil particles moving along the centerline have a time dependent velocity distribution which is expressed as: V=[6(1+0,4x²)(1-0,5t)] 00000 0.3 m Determine the acceleration of an oil particle at x=0,25 m and t 1 seconds.
2. The position of a drone as a function of time is given by *(t) = ( 8 i + 1.5 k) + (-3 î + 2 j) t – 0.5 t2 j The units are missing in the constant coefficients above, i.e., "0.5" should be "0.5 m/s2". Include the correct units on all the constant coefficients in your answers below. a. What is the x-position of the drone as a function of time? b. What is the y-position of the drone as a function of time? c. How far away is the drone from its starting position at t = 3s? d. What is the acceleration vector? е. What is the velocity vector as a function of time? (One way to do this is to take the time derivative of the position vector.) f. Make a sketch of the x, y, and z positions of the drone as function of time. You just need the general shape. time time time
A string with a 10-gram decoration on the end is attached to the rear-view mirror of your friend’s father’s Ferrari. You’re curious about how fast this fancy sports car can accelerate. You decide to measure the acceleration by measuring the angle that the string makes with the vertical when the car is accelerating. Your friend’s father puts the pedal to the metal. Using a protractor, you measure that the angle the string makes with the vertical is 40 while the car is accelerating. What is the acceleration of the Ferrari? [Hints: Choose the decoration as the system for your force diagram. Use the vertical-component equation of Newton’s second law to find the magnitude of the force that the string exerts on the decoration. Then continue with the horizontal-component equation.]
19. A particle is moving on the curve x*y =1. As it passes through the point (2,1/4), the x- coordinate is increasing at a rate of 2 units per second. At what rate is the y-coordinate changing at that time?
A weight is oscillating up and down on spring. It's displacement from rest is given by the function d(t)=sin6t-4cos6t, where d is in centimetres and t is time in seconds. a. what is the rate of change of the displacement after 1s b. Determine the maximum and minimum displacements and when they first occur.
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15.C. Suppose that a car moves one-dimensionally along the x-axis and has position equation given by x = 15-2t², velocity equation v = -4t, and acceleration equation a = -4 all in the standard metric units. = a. Compute its position, velocity and acceleration at 2s b. If the positive direction of the axis is to the right, then state if the car is moving toward increasing position (right) or decreasing position (left) at 2s. c. Draw the car below and draw three vectors: position, velocity, and acceleration at 2s -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 →→→meter 6