Question

При подходе к станции машинист выключил двигатель электропоезда, после чего состав стал двигаться с постоянным ускорением 0,1м/с2. Какова длина перемещения поезда до остановки, если в момент выключения двигателя скорость его была 54 км/ч? Через какое время поезд остановился?

Answer 1

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Answer 2

Calculation of the Distance Traveled by the Train

To calculate the distance traveled by the train before coming to a stop, we can use the equation of motion:

\[s = ut + \frac{1}{2}at^2\]

Where: - s is the distance traveled - u is the initial velocity - t is the time taken - a is the acceleration

Given that the initial velocity of the train is 54 km/h, we need to convert it to m/s:

\[u = 54 \, \text{km/h} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{h}}{3600 \, \text{s}} = 15 \, \text{m/s}\]

The acceleration of the train is given as 0.1 m/s².

Now, we can calculate the time taken for the train to come to a stop. Since the train is decelerating, the acceleration will be negative:

\[a = -0.1 \, \text{m/s²}\]

Using the equation of motion, we can solve for time:

\[0 = 15 \, \text{m/s} + (-0.1 \, \text{m/s²}) \times t\]

Simplifying the equation, we get:

\[0.1t = 15\]

Solving for t, we find:

\[t = \frac{15}{0.1} = 150 \, \text{s}\]

Now, we can calculate the distance traveled by the train using the equation of motion:

\[s = 15 \, \text{m/s} \times 150 \, \text{s} + \frac{1}{2} \times (-0.1 \, \text{m/s²}) \times (150 \, \text{s})^2\]

Simplifying the equation, we get:

\[s = 2250 \, \text{m} - 1125 \, \text{m} = 1125 \, \text{m}\]

Therefore, the length of the train's displacement before coming to a stop is 1125 meters.