A locomotive is accelerating at 2.0 m/s2. It passes through a 20.0-m-wide crossing in a time of 2.8 s. After the locomotive leaves the crossing, how much time is required until its speed reaches 36 m/s?
18
To find the time it takes for the locomotive to reach a speed of 36 m/s after leaving the crossing, we need to use the equations of motion. Since the initial speed and the distance traveled after leaving the crossing are not provided, we can assume that the locomotive starts from rest.
Let's break down the problem into two parts:
Part 1: The crossing
The locomotive passes through a 20.0-meter wide crossing in a time of 2.8 seconds. We can use the equation:
distance = initial velocity * time + (1/2) * acceleration * time^2
Since the initial velocity is zero, the equation simplifies to:
distance = (1/2) * acceleration * time^2
Plugging in the values:
20.0 meters = (1/2) * 2.0 m/s^2 * (2.8 s)^2
Solving for time:
time = sqrt((2 * distance) / acceleration)
time = sqrt((2 * 20.0) / 2.0)
time = sqrt(20.0)
time = 4.47 seconds (rounded to two decimal places)
So, the locomotive takes approximately 4.47 seconds to cross the 20.0-meter wide crossing.
Part 2: Reaching a speed of 36 m/s
After leaving the crossing, the locomotive starts from rest and accelerates at a constant rate of 2.0 m/s^2. We need to find the time it takes to reach a speed of 36 m/s.
We can use the equation:
final velocity = initial velocity + acceleration * time
Since the initial velocity is zero, the equation simplifies to:
final velocity = acceleration * time
Plugging in the values:
36 m/s = 2.0 m/s^2 * time
Solving for time:
time = final velocity / acceleration
time = 36 m/s / 2.0 m/s^2
time = 18 seconds
Therefore, it will take approximately 18 seconds for the locomotive to reach a speed of 36 m/s after leaving the crossing.