Two cars are driving down a straight country road when the driver of the first c

Question

Two cars are driving down a straight country road when the driver of the first car (traveling at a speed of 18 m/s) sees a deer crossing the road in front of her. She quickly applies the brake, causing her car to slow down with a (negative) acceleration of 6 m s-2. The second car is a distance D behind her and is traveling at an initial speed of 32 m/s. Its driver immediately applies his brakes as well - assume at the same time as the driver of the first car - but his car is heavier and his tires are not so good and his car only slows down with a (negative) acceleration 3 m s-2. Find the minimum value of D such that the cars do not collide.

Explanation / Answer

time taken by car 1 to stop :

v = u + at

0 = 18 - 6t1

t1 = 3 sec

distance tarveled by car1: d1 = 18 x3 - 6 (3^2 / 2) = 27 m

and time taken by car 2 to stop, t2 = 32/3 = 10.67 s

distance traveled, d2 = 32 x 10.67 - (3 x 10.67^2 / 2) = 170.67 m

D = d2 - d1   =143.67 m

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