Final answer:
a) It takes 18.26 seconds for the light-rail commuter train to reach its top speed of 84.8 km/hr. b) It takes 19.31 seconds for the train to come to a stop from its top speed. c) The emergency deceleration of the train is -2.95 m/s².
Step-by-step explanation:
a) How long does it take to reach top speed?
To find the time it takes for the train to reach its top speed, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the initial velocity is 0 m/s, the acceleration is 1.29 m/s², and the final velocity is 84.8 km/hr. We first need to convert the final velocity from km/hr to m/s by multiplying it by 1000/3600. Plugging in these values, we get:
84.8 km/hr * (1000 m/1 km) / (3600 s/1 hr) = 23.6 m/s
Now, we can rearrange the formula to solve for time:
t = (v - u) / a
t = (23.6 m/s - 0 m/s) / (1.29 m/s²) = 18.26 s
b) How long does it take to come to a stop speed?
To find the time it takes for the train to come to a stop, we can use the same formula as before, but with a negative acceleration to represent deceleration. In this case, the acceleration is -1.22 m/s² and the initial velocity is 84.8 km/hr. Converting the initial velocity to m/s, we get:
84.8 km/hr * (1000 m/1 km) / (3600 s/1 hr) = 23.6 m/s
Plugging in these values, we get:
t = (0 m/s - 23.6 m/s) / (-1.22 m/s²) = 19.31 s
c) What is its emergency deceleration?
To find the emergency deceleration, we can use the formula a = (v - u) / t, where a is the acceleration, v is the final velocity, u is the initial velocity, and t is the time. In this case, the final velocity is 0 m/s, the initial velocity is 84.8 km/hr, and the time is 8.01 s. Converting the initial velocity to m/s, we get:
84.8 km/hr * (1000 m/1 km) / (3600 s/1 hr) = 23.6 m/s
Plugging in these values, we get:
a = (0 m/s - 23.6 m/s) / 8.01 s = -2.95 m/s²