Question

A train 500 m long is moving on a straight track with a speed of 81.6 km/h. The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 17.9km/h. Assuming constant acceleration, determine how long the train blocked the crossing. Disregard the width of the crossing.s

Answer 1

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

`\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{ = }(-489.23)/(1000) \\ a\text{ = }-0.489m/s^2 \end{gathered}`

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