A train is traveling down a straight track at 25 m/s when the engineer applies the brakes, resulting in an acceleration of −1.0 m/s2 as long as the train is in motion. How far does the train move during a 50 s time interval starting at the instant the brakes are applied?

Question

A train is traveling down a straight track at 25 m/s when the engineer applies the brakes, resulting in an acceleration of −1.0 m/s2 as long as the train is in motion. How far does the train move during a 50 s time interval starting at the instant the brakes are applied?

Answer 1

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Answer 2

To determine the distance the train moves during the 50-second time interval, we can use the following kinematic equation:

𝑑 = 𝑣₀𝑡 + (0.5)𝑎𝑡²

Where:
𝑑 is the distance traveled
𝑣₀ is the initial velocity (25 m/s)
𝑎 is the acceleration (-1.0 m/s²)
𝑡 is the time interval (50 s)

Let's substitute the given values into the equation:

𝑑 = (25 m/s)(50 s) + (0.5)(-1.0 m/s²)(50 s)²

First, calculate the velocity component:
(25 m/s)(50 s) = 1250 m

Next, calculate the acceleration component:
(0.5)(-1.0 m/s²)(50 s)² = -1250 m

Now, substitute the values back into the equation:

𝑑 = 1250 m + (-1250 m)
𝑑 = 0 m

Therefore, the train doesn't move any distance during the 50-second time interval since the positive velocity component cancels out the negative acceleration component.