A subway train starts from rest at a station and accelerates at a rate of until it stops at the next station. Find the distance covered.
xtot=1800m
To find the distance covered by the subway train, we can use the kinematic equation:
x = ut + (1/2)at^2
Where:
x = distance covered (what we want to find)
u = initial velocity (0 m/s, since it starts from rest)
a = acceleration (unknown)
t = time taken to stop (unknown)
Given that the total distance covered by the subway train is 1800 meters (xtot = 1800m), we can split the problem into two parts - the distance covered while accelerating and the distance covered while decelerating.
1. Distance covered while accelerating:
From rest, the train starts to accelerate until it reaches a certain velocity. The time taken for this part can be found using the equation:
v = u + at
where v is the final velocity (unknown).
Since the train starts at rest, u = 0 m/s, and the equation becomes:
v = at
Now, we can solve for the time taken, which is the same for both the acceleration and deceleration parts.
From the given information, we have xtot = 1800m, which includes the distance covered during acceleration and deceleration.
2. Distance covered while decelerating:
After reaching a certain velocity, the train decelerates until it comes to a stop. The time taken for this part can be found using the equation:
v = u - at
where v is the final velocity at stopping (0 m/s).
Since the train's final velocity is zero, the equation becomes:
0 = u - at
Now we can solve for the time taken in the deceleration part.
Once we find the time taken for both acceleration and deceleration, we can substitute these values back into the distance equation to solve for the distance covered by the subway train.
Note: To fully solve this problem, the values for acceleration and time taken are required.