Question

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.

Answer 1

If the track has circumference c miles, then and the car's speeds are x and y mi/s, then since time = distance/speed, 

In the same direction, the slow car has a "lead" of 1 mile which the faster car has to make up. 

1/(y-x) = 120 
1/(x+y) = 30 

120(y-x) = 30(x+y) 
120y-120x = 30x+30y 
90y = 150x 
y = 5/3 x 


1/(x + 5/3 x) = 30 
8/3 x * 30 = 1 
80x = 1 
x = 1/80 mi/sec = 45 mph 
y = 75 mph