Two cars, starting from rest, begin thier trips to a mutual meeting point at the

Question

Two cars, starting from rest, begin thier trips to a mutual meeting point at the same time. Car A travels true east , and accelerates at 6m/s^2, but has a top speed of 55m/s. car B traveks true north and accelerates at 5 m/s^2, but has a top speed of 72 m/s. If car B has been traveling at top speed for 4.7 s when the two cars meet :
A. For how long had each car been traveling?
B. How far away from the meeting point did Car A start?
C. How far away from the meeting point did Car B start?
D. How far away were the cars from each other when they started?

Explanation / Answer

a) car B hit max speed when v=v0+at 72 = 0 + 5t t= 72/5 = 14.4 so total time is 14.4+4.7=19.1 s b) car A will have hit max speed after 55 = 0 + 6 t t= 55/6 = 9.17 s in that time it will travel a distance d=0.5*6*9.17^2=252.3 after max speed it will travel a distance d= 55*(19.1-9.17)=546.2 so total distance 252.3+546.2=798.5 m c) b will travel a distance will acceleration d= 0 + 0.5*5*14.4^2=518.4 then at max speed d= 4.7*72=338.4 total distance= 518.4 +338.4=856.8 m d) distance between = sqrt(856.8^2+798.5^2)=1171.2 m

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