In a quarter-mile drag race, two cars start simultaneously from rest, and each a

Question

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 10.6 m/s2 and a maximum speed of 109 m/s. Car B has an acceleration of 12.0 m/s2 and a maximum speed of 94.2 m/s. (a) Which car wins the race? Type 1 for A, 2 for B. (b) By how many seconds does this car win the race? (a) Number (b) Number Units

Explanation / Answer

for A .. time taken to reach mx speed,t1 = 109/10.6 =10.283 distance travelled in this time d1= V^2/2a = 109^2 /2* 10.6 = 560.4245 the race is of quarter mile ==> 402.33m this means the A completes the race before achieving maximum speed the time taken to complete race is , ta =root( 2d/a) =root( 2*402.33/10.6) ta = 8.71 s for B to reach max speed , t2 = 94.2/12 =7.85 s dist. travelled in time t2 is d' = V^2/2a = 369.735 remaining dist. = 403.22- 369.735 = 32.595 time taken to cover 32.595m is 0.346 s total time tb = 0.346+ 7.85 = 8.196s this says car B will win by (8.71-8.196) = 0.514s

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