Question

Two rather unequal cars are competing in a drag race. For simplicity, let's assume that the accelerations of the cars are constant. Car 1 has an acceleration of 3.9 m/s2, while car 2 has an acceleration of 6.9 m/s2. Car 2 gets off to a late start, 1.1 seconds after car 1. At what time after car 1 took off will it be overtaken by car 2?

Answer 1

for overtaking by car 2 ,

distance travelled by car 1 in t+11sec = distance traveled by car 2 in tsec

1/2*a1*(t+1.1)^2 = 1/2*a2*t2

1/2*3.9*(t^2+1.21+2.2t) = 1/2*6.9*t^2

after arranging,we get quadratic in t,

10t^2.2t-15.73+0

after solving,we get,t=2.7(approx)

T=2.7+1.1=3.8sec(approx)