Question

A light-rail commuter train accelerates at a rate of 1.35 m/s. D A 33% Part (a) How long does it take to reach its top speed of 85 km/h, in seconds, starting from rest? Hints deduction per hint. Hints remaining 1 Feedback: deduction per feedback A 33 Part (b) The same train ordinarily brakes at a rate of 1.8 m/s. How long does it take to come to a stop, in seconds, from its top speed? 433 Part (c) In emergencies the train can slow more rapidly. coming to rest from 85 km/h in 7.9 5. What is the magnitude of the acceleration during emergency braking, in meters per square second?

Answer 1

a) 17.49 seconds

b) 13.12 seconds

c) 2.99 m/s²

Step-by-step explanation:

a) Acceleration = a = 1.35 m/s²

Final velocity = v = 85 km/h =
`85(1000)/(3600)=23.61\ m/s`

Initial velocity = u = 0

Equation of motion

`v=u+at\\\Rightarrow 23.61=0+1.35t\\\Rightarrow t=(23.61)/(1.35)=17.49\ s`

Time taken to accelerate to top speed is 17.49 seconds.

b) Acceleration = a = -1.8 m/s²

Initial velocity = u = 23.61\ m/s

Final velocity = v = 0

`v=u+at\\\Rightarrow 0=23.61-1.8t\\\Rightarrow t=(23.61)/(1.8)=13.12\ s`

Time taken to stop the train from top speed is 13.12 seconds

c) Initial velocity = u = 23.61 m/s

Time taken = t = 7.9 s

Final velocity = v = 0

`v=u+at\\\Rightarrow 0=23.61+a7.9\\\Rightarrow a=(-23.61)/(7.9)=-2.99\ m/s^2`

Emergency acceleration is 2.99 m/s² (magnitude)