The time needed by the train is 40 s
Explanation:
The acceleration of an object is given by the equation:
[tex]a=\frac{v-u}{t}[/tex]
where
v is the final velocity
u is the initial velocity
t is the time
For the train in this problem, we know that:
u = 0 is the initial velocity (it starts from rest)
[tex]v=72 km/h\cdot \frac{1000 m/km}{3600 s/h}=20 m/s[/tex] is the final velocity
[tex]a=0.5 m/s^2[/tex] is the acceleration
Solving for t, we find the time the train needs to accelerate at that velocity:
[tex]t=\frac{v-u}{a}=\frac{20-0}{0.5}=40s[/tex]
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