Kevin S. Huang

2013: Problem 1

Topic: Kinematics
Concepts: 5 kinematics equations

Solution:

Let each car have length $L$ . If the train has acceleration $a$ , then it takes time $t_1$ where

L=\frac{1}{2}at_1^2

t_1=\sqrt{\frac{2L}{a}}

for the first car to pass the observer. Since $t \propto \sqrt{L}$ , the time $t_{10}$ it takes the first 10 cars to pass the observer is

t_{10}=\sqrt{10}t_1

Similarly, the time $t_9$ it takes the first 9 cars to pass the observer is

t_9=\sqrt{9}t_1

The time is takes the 10th car to pass is the difference in times:

t_{10}-t_9=(\sqrt{10}-\sqrt{9})t_1=(\sqrt{10}-\sqrt{9})(5\,\mathrm{s})=0.81\,\mathrm{s}

so the answer is E.