Question

Homework 02 (Chapter 02) Problem 2.54 く) 90f 10 〉 Review You are at a train station, standing next to the train at the front of the first car. The train starts moving with constant acceleration, and 4.0 s later the back of the first car passes you. PartA How long does it take after the train starts moving until the back of the seventh car passes you? All cars are the same length. Express your answer with the appropriate units tal Value Units Submit Request Answer Provide Feedback Next>

Answer 1

Let us assume the length of each car is L.

From kinematics we have

$S = vt + 0.5at^2$

here v= 0 as the train starts from rest.

given that it takes 4 seconds for the first car passing.

Hence,

$L= 0.5a4^2 = 8a$

for 7 cars

$7L= 0.5at^2 \\ t = \sqrt{7L/0.5a} = \sqrt{7L/(0.5*(L/8))} =\sqrt{7*8/0.5} = 10.58s$

Hence it takes 10.58 seconds for 7th car to pass.