Kinematics: Would you help me find the solution?

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Kinematics: Would you help me find the solution?

Two trains are on the same track and moving the same direction. Train 1 is behind train 2 and has velocity $30 m s^{- 1}$ $30 ms^(-1)$ . Second train has a velocity $9 m s^{- 1}$ $9 ms^(-1)$ . When the driver of first train saw a train in front of him, he push the brake system with acceleration $1.2 m s^{- 2}$ $1.2 ms^(-2)$ . The distance between these two trains is 180 meters. Do these two trains hit?

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Answer 1 · 2018-02-13T20:08:44

$please look at the explanation section.$ $"please look at the explanation section."$

Explanation:

$the time required for train-1 to stop.$ $"the time required for train-1 to stop."$
$v = v_{i} - a t$ $v=v_i-at$
$0 = 30 - 1.2 t$ $0=30-1.2t$

$t = \frac{30}{1.2} = 25 sec$ $t=30/1.2=25 sec$
$the time required for train-1 to slow down to 9 \frac{m}{s} :$ $"the time required for train-1 to slow down to 9 " m / s:$

$9 = 30 - 1.2 t$ $9=30-1.2t$

$1.2 t = 30 - 9$ $1.2t=30-9$

$1.2 t = 21$ $1.2t=21$

$t = \frac{21}{1.2} = 17.5 sec$ $t=21/(1.2)=17.5 sec$

$displacement of train-1 for 17.5 sec.$ $"displacement of train-1 for 17.5 sec."$

$x_{1} = v_{i} t - \frac{1}{2} a t^{2} = 30 \cdot 17.5 - \frac{1}{2} \cdot 1.2 \cdot {(17.5)}^{2} = 341.25 m$ $x_1=v_it-1/2 a t^2=30*17.5-1/2*1.2*(17.5)^2=341.25" "m$

$displacement of train-2 for 17.5 sec.$ $"displacement of train-2 for 17.5 sec."$

$x_{2} = 180 + 9 \cdot 17.5 = 337.5 m$ $x_2=180+9*17.5=337.5" "m$

$train-1 hits to train-2 because x_{1} > x_{2} .$ $"train-1 hits to train-2 because "x_1>x_2."$

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Kinematics: Would you help me find the solution?

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