A subway train starts from rest at a station and accelerates at a rate of 1.95m/s^2 for 18.4 s. It runs at a constant speed for 68.2 s, and slows down at a rate of -3.539m/s^2 until it stops at the next station. What is the total distance covered?

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Answer 1 · 2018-06-11T06:43:01

Please see the explanation below

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The total distance covered is the area under the $v=f(t)$ curve

$v_1=at=1.95*18.4=35.88ms^-1$

$t_3=(v-u)/a=(0-35.88)/(-3.539)=10.14s$

Total distance (area of $2$ triangles and $1$ rectangle) is

$d=(1/2*35.88*18.4)+(35.88*68.2)+(1/2*35.88*10.14)$

$=330.1+2447+181.9$

$=2959m$

It is the same answer.