Answer :
Answer:
Required time t=5.8s
Explanation:
Given data
Acceleration a=3.08 m/s²
Speed v=29.4 m/s
Required
How much time t is required
Solution
As the train passes through the crossing its motion is described by:
[tex]v=v_{o}+at\\v-v_{o}=at\\and\\x=\frac{1}{2}(v+v_{o})t\\v+v_{o}=\frac{2x}{t}\\ So\\v=\frac{1}{2}(at+\frac{2x}{t} ) \\[/tex]
Substitute the given values
So
[tex]v=\frac{1}{2}((3.08m/s^2)(2.93s)+\frac{2(20.8m)}{2.93s} )\\v=11.61m/s[/tex]
So time required can be calculated by:
[tex]t=\frac{v-v_{o}}{a} \\t=\frac{29.4m/s-11.61m/s}{3.08m/s^2}\\ t=5.8s[/tex]
Required time t=5.8s