Question

Two automobiles are involved in a race over level ground. Both cars begin at rest. The Andi accelerates ar 4 for T seconds and then travels at constant velocity for the rest of the race. The Buick accelerates at A/2 for 27 seconds and then travels at constant velocity for the rest of the race. Determine the distance (d) between the two cars, at the instant ? - 2T, as a function of A and T. Motion Diagram SOCKS a BA 20 Motion Information Object:Art Event 1: Event 2: Object: Buck Event 3: Event 1: Event 2: Event 3: 1-2T -O t: - SYT - 2T 10 V, V 4 aiz 12 A a Mathematical Analysis Audi 27 Audi Questions A-0 m/s, what should d equal? Does your function agree with this observation? Assume the race takes longer than 27 to finish. What is the difference in speed between the two cars as they cross the finish line? Assume the race takes longer than 2T to finish. What is the distance between the two cars as they cross the finish line? -59

Answer 1

Audi Buick UB=0 -0 a А 9= A/2 m/3² for 27 seconds a А = A m/s² for T seconds Velocity of Audi after a seconds Neart rautat m/s AT V= Of A.T А Distance vovered by Andi in T seconds 2 SAP = UT * £ aq 72 OXT+ 2 Ag² Distance covered 7 and 28 seconds SAI covered by Š AT metre Audin between S A2 \x(2T-7) – ATXT = AT A metre

2 ... The total distance covered by Audi in 27 seconds SA = 5 + 5 Al A2 1 --- SA = 1/2 AT² + AT² SA= 2 2 AT metre * Distance covered by Buick in 21 seconds S₂ = 4 x 2T + 2 a 273² Sp = 0X2T + 1 (A) (492) SB = A7² metre ,: The distance d between the cars al- the instant t= 2T is d= SA-SB = 3/4 AT - AT² d = È At² metre:

1 If A=0, A=o, as vitially mihally ball cars are at rest, botts will stay at the same place where they are at t=0 seconds. so distance in such a case after 27 seconds will be zero. If we substitute to A=0 in the enpression for d CŽAT²), it will also give the same answer. I say by sure that our So we can function agree with the observation.

Velocity of Buick after 21 seconds AT m/s Also, Vo = Up + as (27) 48 = 0 + (4) 27 VB we know that the relocity of Audi after I seconds will be a constant and it will be "A = AT m/s So if the race takes longer than 27 seconds then the difference in the speed of the two cars upon crossing line will be zero. As VB=VA = 16 - "A = 0 the finishing m/s av=V

time 2T seconds and it will be After 25 seconds, the two cars with be travelling at the same speed and so will be covering the same distance in equal intervals of time. So the distance between the ears after 27 seconds will be a constant evers upto the finishing line. This constant. distance between the cars is, that have distance they gained by the d=Ź AT² metre as we calculated at the initial stage. The distance between the cars, as they cross the finish line, in a longer tham 27 seu econds race is Ž AT metre