a train slows down as it rounds a sharp horizontal torn, going from 90km/hr to 50km/hr in the 15s it takes to round and bend. The radius of the curve is 150m. Compute the acceleration at the moment the train speed reaches 50km/hr. Assume the train continues to slow down at this time in the same rate.
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Explanation:
First and foremost, we need to consider both the linear decelaration ( from to 90 to 50 km/hr) as well as the centrifugal acceleration experienced by the train while negotiating the bend. This is why the question mentions the value of the radius - 150 m.
Linear decelaration 90 km/hr = 25 m/s, 40 km/hr = 11.11/m/s
a=(v-u)/t
= (25 - 11.11)/15 = 0.926 m/s or - 0.926 m/s as per sign notation = a1
Centrifugal acceleration = (v2)/r
= (11.11)^2/150 = 0.823 m/s = a2
Now since the two forces are at right angles to each other, the magnitude = sqroot( a1^2 + a2^2)= sqroot (0.857 +0.677) = 1.23 m/s
Magnitude = 1.23 m/s. Please find the direction of the force by vector diagram
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