A subway train starts from rest at a station and accelerates at a rate of 1.60 m/s^2 for 14.0 s . It runs at constant speed for 70.0 s} and slows down at a rate of 3.50m/s^2 until it stops at the next station.
Find the total distance covered.
1881.6
To find the total distance covered by the subway train, we need to calculate the distances covered during each stage of its motion (acceleration, constant speed, and deceleration) and then add them up.
1. Acceleration stage:
The formula we can use to calculate the distance covered during the acceleration stage is:
distance = (initial velocity × time) + (1/2 × acceleration × time^2)
Given:
Acceleration (a) = 1.60 m/s^2
Time (t) = 14.0 s
Since the subway train starts from rest (initial velocity = 0), the equation becomes:
distance = (0 × 14.0) + (1/2 × 1.60 × (14.0)^2)
distance = 0 + (0.5 × 1.60 × 196.0)
distance = 0 + 156.80
distance = 156.80 m
2. Constant speed stage:
During this stage, the subway train runs at a constant speed for 70.0 s. The distance covered at a constant speed is given by:
distance = speed × time
Since the speed remains constant, we can directly calculate the distance:
distance = speed × time = 0 m/s × 70.0 s = 0 m
3. Deceleration stage:
Using the same formula as the acceleration stage, the distance covered during deceleration is:
distance = (initial velocity × time) + (1/2 × acceleration × time^2)
Given:
Acceleration (a) = -3.50 m/s^2 (negative because it's deceleration)
Time (t) = the time it took to slow down to 0 m/s
To calculate the time it took to slow down, we can use the formula:
final velocity = initial velocity + (acceleration × time)
Since the final velocity is 0, we can solve for time:
0 = initial velocity + (-3.50 × time)
initial velocity = 3.50 × time
Substituting the value of initial velocity in the distance formula:
distance = (3.50 × time × time) + (1/2 × -3.50 × time^2)
distance = 3.50 × time^2 - 1.75 × time^2
distance = 1.75 × time^2
To find the time it took to slow down, we need more information or an additional equation. Please provide the necessary information or equation and we can continue the calculation.
In summary, we have calculated the distance covered during the acceleration stage (156.80 m) and at a constant speed (0 m). However, we need more information or an equation to calculate the distance covered during deceleration and, consequently, the total distance covered.