An RPI freshmen, inexperienced with suburban traffic officers, has just recieved

Question

An RPI freshmen, inexperienced with suburban traffic officers, has just recieved a ticket for speeding. Thereafter, when the freshmen comes upon one of the "speedometer test" sections on a level stretch of highway, the student decides to check the speedometer reading. As the student passes to "O"start of the marked section, the student depresses the accelerator and for the entire period of the test the student holds the car at constant acceleration. As the student passes the 0.10 mi post the recorded time is 16 s after starting the test, and 0.8 s later the student then passes the 0.2 mi post.
a) what should the speedometer have read at the .20mi post?
b) find the acceleration

Explanation / Answer

s = ut + 1/2*at2

0.1 = u*1.6 + 1/2*a*1.62 or 0.1 = u*1.6 + a*1.28

0.2 = u*(1.6+0.8) + 1/2*a*(1.6+0.8)2 or 0.2 = u*2.4 + a*2.88

Solving both these equations, u = 0.052 mi/s and a = 0.013 mi/s2

a) Speedometer reading at 0.2 mi is (v = u + at) v = 0.052 + 0.013*(1.6+0.8) = 0.0833 mi/s = 0.0833*3600 mi/hr = 299.7 mi/hr

b) Acceleration a = 0.013 mi/s2 = 0.013*5280 ft/s2 = 68.6 ft/s2

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