Special sections of roadway are sometimes paved with \"rumble strips\" to alert

Question

Special sections of roadway are sometimes paved with "rumble strips" to alert inattentive drivers. In a particular case the grooves are spaced L = 0.26 m apart and the depth of each groove is d = 0.95 cm. As you drive over this rumble strip, the tires of your car oscillate about their equilibrium positions with a frequency of f = 61 Hz. Refer to the figure, which is not drawn to scale. Enter an expression that describes the vertical position, y(t), of one of the car tires as a function of time, t in terms of the defined quantities. Assume the motion is sinusoidal, with its argument in radians and the positive y-axis up. Take the tire's equilibrium position as y = 0 and take y(0) = 0 and increasing. Find the vertical position of the tire, in centimeters, at the time t = 2.5 s. With your tire oscillating at a frequency of = 61 Hz and the distance between grooves L = 0.26 m, what is the of your car, in kilometers per hour ?

Explanation / Answer

Here ,

v = L * f

v = 61 * 0.26 m/s

v = 15.9 m/s

v = 57.1 km/hr

the speed of the car is 57.1 km/hr

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