In: Physics
1.a)
Let us consider the motion of the train for the first 15.90 seconds.
We have:
Initial velocity
because it starts from rest
Acceleration
Time
We have the equation of motion for the final velocity
given by:
Substituting the values:
This is the speed of the time when it stops accelerating. Since
it then runs at a constant speed until it starts slowing down, the
speed of the train just before it starts slowing down is equal to
it. Therefore,
b)
Let us now consider the motion of the train from when it starts slowing down until it stops at the next station.
We have:
Initial velocity
which is the velocity when it starts slowing down
Final velocity
because it comes to rest at the station
Acceleration
where the minus sign indicates that it is slowing down.
Let us again use the equation
Rearranging for the time,
Substituting,
This is the time for which it slows down
The total time taken to finish the trip is the sum of the time spent accelerating, time it runs at constant speed and the time it slows down.
Therefore,
The total trip time is 59.73s