A locomotive is accelerating at 1.6 m/s2 as it passes through a 30-m-wide crossing. After the...

A locomotive is accelerating at 1.6 m/s2 as it passes through a 30-m-wide crossing. After the locomotive leaves the crossing, how much time is required until its speed reaches 40?

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Expert Solution

In the question it is not given wether the car is starting from rest as it leaves the crossing or it starts fro rest at the beginning of the crossing. So I'm giving the solutions to both those cases.

Case 1 : Assuming that the locomotive is starting from rest, as it passes through the crossing, the acceleration is a = 1.6 m/s². Initial velocity u = 0 m/s(starting from rest), the final velocity required is v = 40 m/s. So from the kinematics equation v = u + at, t = v/a = 40/1.6 = 25 sec. So the time required is t = 25 sec.

Case 2 : Now assume that car is starting from rest at one end of the 30 m wide crossing, so the speed at the start of crossing is u = 0 m/s, let the speed at the end of crossing i.e when the car leaves the crossing be v m/sec. From kinematics equation v²-u² = 2as, v = = (2*1.6*30)^(1/2) = 96^0.5 = 9.798 m/s. Now we have to find the time required from this moment on to reach a final speed of 40 m/s. Now from v = u +at, but this time v = 40 m/s, u = 9.798 m/s, a = 1.6 m/s², so t = = (40-9.798)/1.6 = 18.876 sec. So in this case the time required is t = 18.876 sec.

genius_generous answered 1 year ago

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