A motorist travelingalong a straight portion of a highway is decreasing the spee

Question

A motorist travelingalong a straight portion of a highway is decreasing the speed of his automobile at a constant rate before existing from the highway into a circular exit ramp with a radius of 560-ft. he continue to decelerate at the same constant rate so that 10s after entering the ramp, his speed has decreased to 20mi/h, a speed which he then maintains. Knowing that at this constant speed the total acceleration of the automobile is equal to one-quarter of its value prior to entering the ramp, determine the maximum value of the total acceleration of the automobile.

Explanation / Answer

a = v^2/r. 20 mph = 29.333 ft/s 29.333 ft/s ^2 / 560 feet = 1.536 ft/s^2 acceleration. 1.536 * 4 = 6.144 ft/s^2 right before getting on the ramp. v = v0 + a*t Solve for v0 v0 = 29.333 - (-6.144*10) = 90.773 ft/s v^2/r = 90.773 ^2 / 560 = 14.714 ft/s^2 Apply pythagoreans theorem: a^2 = b^2 + c^2 = 6.144^2 + 14.714^2 a^2 = 254.250 a = 15.945 ft/s^2

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