The LRT train in Edmonton starts from rest at the Clareview station and accelerates at a rate of 4.0 m/s^2 for the first 6.0s. The train then maintains a constant speed for the next 45.0s.
If the next station is 3.0km from Clareview station, calculate the time it takes for this train to pass by this check point.
First, let's calculate the distance traveled during the acceleration phase:
Using the formula:
$v = u + at$
where:
v = final velocity (constant speed)
u = initial velocity (0 m/s)
a = acceleration (4.0 m/s^2)
t = time (6.0 s)
We can calculate the final velocity:
$v = 0 + (4.0)(6.0) = 24.0 m/s$
Next, we calculate the distance traveled during acceleration using the formula:
$s = ut + 0.5at^2$
$s = (0)(6.0) + 0.5(4.0)(6.0)^2$
$s = 0 + 0.5(4.0)(36.0)$
$s = 0 + 0.5(144.0)$
$s = 0 + 72.0$
$s = 72.0 m$
Now, let's calculate the distance traveled during the constant speed phase:
Distance = 3000m - 72m = 2928m
Now, we calculate the time it takes for the train to pass the checkpoint during the constant speed phase:
Time = Distance / Speed = 2928m / 24.0 m/s = 122s
Adding the time taken for acceleration:
Total time = 6.0s + 122s = 128s
Therefore, it takes 128 seconds for the train to pass the 3.0km checkpoint.