a train starts from rest and accelerates unifotmly, until it has travled 3.7 km and acquired a velocity of 30 m/s. the train then moves at a constant velocity of 30 m/s for 410 s. the train then slows down uniformly at 0.065 m/s^2, until it reaches a halt. what distance does the train travel while it is slowing down
See previous post.
To find the distance the train travels while it is slowing down, we need to determine how long it takes for the train to come to a halt.
Let's break down the problem step by step:
Step 1: Determining acceleration during the first phase
The train starts from rest and accelerates uniformly until it reaches a velocity of 30 m/s. We can use the following formula to find the acceleration:
v = u + at
Where:
v = final velocity = 30 m/s
u = initial velocity = 0 m/s
a = acceleration (unknown)
t = time taken to reach 30 m/s (unknown)
Since the train starts from rest (u = 0 m/s), the formula simplifies to:
30 = 0 + a * t
30 = a * t
Step 2: Determining the time taken during the first phase
We know that the train has traveled a distance of 3.7 km. We can use the following formula to find the time taken during the first phase:
s = ut + 0.5at^2
Where:
s = distance traveled = 3.7 km = 3700 m
u = initial velocity = 0 m/s
a = acceleration (from step 1)
t = time taken (unknown)
Using the formula with the known values:
3700 = 0.5 * a * t^2
Step 3: Determining the time taken during the second phase
The train moves at a constant velocity of 30 m/s for 410 seconds.
Step 4: Determining the deceleration during the third phase
The train slows down uniformly at a deceleration of 0.065 m/s^2.
Step 5: Determining the time taken during the third phase
We can use the formula: v = u + at, where u = 30 m/s, v = 0 m/s, a = -0.065 m/s^2 (negative because it's deceleration), and t = time taken (unknown) to find the time taken during the third phase.
Step 6: Calculating the distance traveled during the third phase
Using the formula: s = ut + 0.5at^2, where u = 30 m/s, a = -0.065 m/s^2, and t = time taken (from step 5).
We can follow these steps to find the distance the train travels while slowing down.