What is the distance traveled by the train in kilometers?

Question

A train starts from rest and accelerates uniformly, until it has traveled 2.1 km and acquired a velocity of 24 m/s. The train then moves at a constant velocity of 24 m/s for 400 s. The train then slows down uniformly at 0.065 m/s^2, until it is brought to a halt. What is the distance traveled by the train in kilometers?

Answer 1

The train goes 2.1 km first

 

then goes with constant speed of 24m/s for 400s

so  distance=V x t= 24 x 400 = 9600m that means 9.6km

 

then it slows down from 24m/s to 0

so it takes 

V_f- V₀=at

0-24=-0.065 xt   => t=369.23 s

that means it will go the distance of

distance= V₀t+1/2 gt²=24 x 369.23-1/2( 0.065 x 369.23)=8849.52m  that means 8.8km

so in total 2.1+9.6+8.8=20.5km

 

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