Two racecars are driving at constant speeds around a circular track. both cars are the same distance away from the center of the
track, but car 2 is driving twice as fast as car 1. the acceleration of car 2 is ___________ the acceleration of car 1.
1 answer:
If the track has circumference c miles, then and the car's speeds are x and y mi/s, then since time = distance/speed,
<span>In the same direction, the slow car has a "lead" of 1 mile which the faster car has to make up. </span>
<span>1/(y-x) = 120 </span>
<span>1/(x+y) = 30 </span>
<span>120(y-x) = 30(x+y) </span>
<span>120y-120x = 30x+30y </span>
<span>90y = 150x </span>
<span>y = 5/3 x </span>
<span>1/(x + 5/3 x) = 30 </span>
<span>8/3 x * 30 = 1 </span>
<span>80x = 1 </span>
<span>x = 1/80 mi/sec = 45 mph </span>
<span>y = 75 mph</span>
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