Respuesta :
Answer:
The train blocked the road for 36.2 seconds
Explanations:The length of the train is the distance (s)
s = 500 m
The initial velocity, u = 81.6 km/h
u = 81.6 x (1000/3600)
u = 22.67 m/s
The final velocity, v = 17.9 km/h
v = 17.9 x (1000/3600)
v = 4.97 m/s
Since the train applied brake and slowed down, it is expected to have a negative acceleration.
Calculate the acceleration using the equation of motion below
[tex]\begin{gathered} v^2=u^2\text{ + 2as} \\ 4.97^2=22^{}.67^2\text{ + 2a(500)} \\ 24.7\text{ = }513.93\text{ + 1000a} \\ 1000a\text{ = }24.7\text{ - 513.93} \\ 1000a\text{ = }-489.23 \\ a\text{ = }\frac{-489.23}{1000} \\ a\text{ = }-0.489m/s^2 \end{gathered}[/tex]To find the time taken for the train to block the crossing, use the formula below:
v = u + at
Substitute v = 4.97, u = 22.67, and a = -0.489 into the equation v = u + at
4.97 = 22.67 + (-0.489)t
0.489t = 22.67 - 4.97
0.489t = 17.7
t = 17.7 / 0.489
t = 36.2 seconds
The train blocked the road for 36.2 seconds
