A subway train starts from rest at a station and accelerates at a rate of 1.60 m/s for
14.0s. It runs at constant speed for 70.0s and slows down at a rate of 3.50 m/s until it stops at the next station. Find the total distance covered?
To find the total distance covered, we need to calculate the distance covered during each interval of motion (acceleration, constant speed, deceleration) and then add them together.
1. Distance covered during acceleration:
Using the equation for distance traveled during constant acceleration, we have:
distance = 0.5 * acceleration * time^2
distance = 0.5 * 1.60 m/s^2 * (14.0s)^2
distance = 0.5 * 1.60 m/s^2 * 196s^2
distance = 156.8 meters
2. Distance covered during constant speed:
The train is traveling at a constant speed, so the distance covered is simply the product of speed and time:
distance = speed * time
distance = 1.60 m/s * 70.0s
distance = 112 meters
3. Distance covered during deceleration:
Again using the equation for distance traveled during constant acceleration, we have:
distance = 0.5 * acceleration * time^2
distance = 0.5 * (-3.50 m/s^2) * (14.0s)^2 (negative acceleration due to deceleration)
distance = 0.5 * (-3.50 m/s^2) * 196s^2
distance = -343 meters (negative sign indicates direction opposite to initial motion)
Now we can find the total distance covered:
total distance = distance during acceleration + distance during constant speed + distance during deceleration
total distance = 156.8 meters + 112 meters - 343 meters
total distance = -74.2 meters
The total distance covered by the subway train is -74.2 meters. Note that the negative sign indicates that the train moves in the opposite direction from the initial motion.