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(D) Let the initial speed of each train be $u = 40\, m/s$. Since the trains are $2.0\, km$ $(2000\, m)$ apart and they are moving towards each other w

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$0.8$

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(D) Let the initial speed of each train be $u = 40\, m/s$. Since the trains are $2.0\, km$ $(2000\, m)$ apart and they are moving towards each other with equal speeds,each train must cover a distance of $s = 1000\, m$ to come to a stop just before colliding. Using the kinematic equation $v^2 = u^2 + 2as$,where $v = 0$ (final velocity),$u = 40\, m/s$,and $s = 1000\, m$: $0^2 = (40)^2 + 2 \cdot a \cdot 1000$ $0 = 1600 + 2000a$ $2000a = -1600$ $a = -\frac{1600}{2000} = -0.8\, m/s^2$. The magnitude of the deceleration is $0.8\, m/s^2$.

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