A train is traveling down a straight track at 25 m/s when the engineer applies the brakes, resulting in an acceleration of β1.0 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?
dasdasasas
To determine the distance the train moves during the 50-second time interval, we can use the following kinematic equation:
π = π£βπ‘ + (0.5)ππ‘Β²
Where:
π is the distance traveled
π£β is the initial velocity (25 m/s)
π is the acceleration (-1.0 m/sΒ²)
π‘ is the time interval (50 s)
Let's substitute the given values into the equation:
π = (25 m/s)(50 s) + (0.5)(-1.0 m/sΒ²)(50 s)Β²
First, calculate the velocity component:
(25 m/s)(50 s) = 1250 m
Next, calculate the acceleration component:
(0.5)(-1.0 m/sΒ²)(50 s)Β² = -1250 m
Now, substitute the values back into the equation:
π = 1250 m + (-1250 m)
π = 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.