Question

Differential Equations Question

1 Two drivers, Alison and Kevin, are participating in a race. Beginning from a standing start, they each proceed with a constant acceleration. Alison covers the last 7 of the distance in 3 seconds, whereas Kevin covers the last of the distance in 7 seconds. Who wins and by how much time? Kevin wins the race by seconds. (Type an integer or decimal rounded to the nearest tenth as needed.)

Answer 1

solution :- Acceleration is constant let it is a. Speed is integration of acceleration and initial ispeed is o at t=0 ) V= at & Abscissa is integration of speed. Let's take to at t=0 X= at? Let I be the distance to be covered during Mace to (D) = 20 The duration for veace for Alison is :- where AA = Acceleration of Alison . We tenow that Alison covered lost it of distance in 3 sec. The dweation for Alison to reach distane ta (90) QX6D ill RD an 70A 6X2D 7 AA F AG) Alison cover last – of distance is Sta = ta (0) - tn (fo = tako) [ 1 - 1

ta 6) = Sta 1. V6 7 = U7 X3 7 5183 157 +46) (2-649)x3 [2.6454 0.449) ンテール 40.42 ava Similarly for Kevin: tolo) = 20 1199) - Voxto - v 16) StB = to (o) -to (28) - to (o) [ 2 - 1 3 too) = StB xu3 £3-12 = 7X03 (13+ (2) = TX 7732 (1.730 + F414 414) 38.142 Kevin take cless to complete his race. Hence Kevin tuin by (40-47-38-14) 2.28 seconds
Kevin will take less time to complete his race. Hence Kevin will win by 2.28 seconds.