a car travels on a flat circular road of radius R. At a certain instant the velo

Question

a car travels on a flat circular road of radius R. At a certain instant the velocity of the car is 24m/s west, and the total acceleration of the car is 2.5 m/s2 53 degrees north of west. find the radial and tangential components of the acceleration of the car. how long will it take for the car to make a one full circle from the point at which its velocity is 24m/s west?

Explanation / Answer

the tangential accel at that point is 2.5 cos 53 = 1.5m/s/s to the west the radial component of accel is 2.5 sin 53 = 2.0m/s/s to the center of the circle (south) knowing that centripetal accel = v^2/r, we can find the radius of the circle: 2.0m/s/s = (24m/s)^2/r => r=288m so that a total circuit covers a distance of 2 pi*288m = 1808.6m thus we have that dist = v0t+1/2at^2 or 1808.6 = 24 t+1/2(1.5)t^2 this is a quadratic in t, solve using normal techniques, (I get t=35.6 s)

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