Your state's Driver Handbook says, "When the vehicle ahead of you passes a certain point such as a sign, count 'one-thousand-one, one-thousand-two, one-thousand-three.' This takes about three seconds. If you pass the same point before you finish counting, you are following too closely." In your car, you are following a truck on the highway, both of you moving at \(100 \mathrm{~km} / \mathrm{h}\). You are keeping a 3. 0-s gap between your front bumper and the rear of the truck. Suddenly a large box appears on the road beneath the rear of the truck. Apparently the truck's axles were tall enough to allow it to pass right over the object, but yours are not! It takes you \(0.75 \mathrm{~s}\) to react and hit your brakes.

(a) What is the minimum constant acceleration required if you are not to hit the box?

(b) What would your answer be if you were keeping a 2. 0-s gap between your car and the truck, as is sometimes recommended as safe, under optimal driving conditions, for alert, experienced drivers with good reflexes? Compare and comment on your answers in parts \(a\) and b.