**87. ssm In a quarter-mile drag race, two cars start simultaneously from rest, and each accelerates at a constant rate until it either reaches its maximum speed or crosses the finish line. Car A has an acceleration of 11.0 m/s2 and a maximum speed of 106 m/s. Car B has an acceleration of 11.6 m/s2 and a maximum speed of 92.4 m/s. Which car wins the race, and by how many seconds?

 

First convert length of track to metric

 

 

There are two possibilities with the cars, they either cover the distance before they reach max speed, in that case we can calculate one time interval  using

 

Since   so total time is found by

 

But if the car reaches max speed before it finishes the track, we have two time intervals.  The time to reach max speed and then the time the car travels at max speed to finish the track.  For that part we would use

So the time is found by

 

So first see if either car reaches max speed before the end of the track.  So calculate the distance required to reach max speed using

 

Since   so total distance is found by

 

Car A

 

So Car A will finish course before achieving max speed!  We only need one time interval

 

Car B

 

Car B will achieve max speed before finishing course so we will need to calculate two time intervals.

 

Find time for Car A

 

Car B will travel 368.0 m to achieve max speed, then it will need to travel the remainder of the distance (402.3 m – 368.0 m = 34.3 m) at its max speed of 92.4 m/s.

 

 

 

 

 

 

Car B wins the race by 0.21 s

 

 

Please send any comments or questions about this page to ddonovan@nmu.edu

This page last updated on January 11, 2020