Two cars are moving at \(97 \mathrm{~km} / \mathrm{h}\), one behind the other, on a rural road. A deer jumps in front of the lead car, and its driver slams on the brakes and stops. What minimum initial distance between the rear of the lead car and the front of the second car is required if the second car is to stop before hitting the lead car? Assume that the acceleration is the same for borh cars and that the driver of the second car begins braking \(0.50 \mathrm{~s}\) after the lead car begins braking.