A train is traveling down a straight track at 25 m/s when the engineer applies the brakes, resulting in an acceleration of ā1.0 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?
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To determine the distance the train moves during the 50-second time interval, we can use the following kinematic equation:
š = š£āš” + (0.5)šš”Ā²
Where:
š is the distance traveled
š£ā is the initial velocity (25 m/s)
š is the acceleration (-1.0 m/sĀ²)
š” is the time interval (50 s)
Let's substitute the given values into the equation:
š = (25 m/s)(50 s) + (0.5)(-1.0 m/sĀ²)(50 s)Ā²
First, calculate the velocity component:
(25 m/s)(50 s) = 1250 m
Next, calculate the acceleration component:
(0.5)(-1.0 m/sĀ²)(50 s)Ā² = -1250 m
Now, substitute the values back into the equation:
š = 1250 m + (-1250 m)
š = 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.