Bicycle Times
For what time interval is the bicycle ahead of the car?
As soon as a traffic light turns green, a car speeds up from rest to 52 mi/ h with constant acceleration 10 mi/ h-s. In the adjoining bike lane, a cyclist speeds up from rest to 23 mi/ h with constant acceleration 12 mi/ h-s. Each vehicle maintains constant velocity after reaching its cruising speed.
For what time interval is the bicycle ahead of the car?
The cyclist will be at his maximum speed in 23/12 seconds (1.91666)
The car will be at his maximum speed in 5.2 seconds
The cyclist has traveled ½ * 12 * (23/12)^2 = 22.0416666 m in that time ( s(t)=½at^2 )
the formula for the traveled distance of the cyclist after 1.91666 seconds is y = -22.041666 + 23x
And the formula for the traveled distance of the car (up to x = 5.2 seconds) is y = ½ * 10x^2
These formulas intersect.
-22.041666 + 23x = ½ * 10x^2
Your graphing calculator can solve it (I’m too lazy)
They intersect at x = 3.2389711
This answer is below the 5.2 seconds so it is correct
The bicycle is ahead of the car for 0 < x < 3.2389711
Dirt Rag TV Interbike 2008 (Bicycle Times)
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