A train travels in 3 minutes a distance of 3.15 km from rest at one station to rest at another station. It is uniformly accelerated for the 1st 30 seconds and uniformly retarded for the last 15 seconds, the speed being constant for the remaining time. Find the maximum velocity, acceleration and retardation. Use v-t graph to solve th problem.

A train travels in 3 minutes a distance of 3.15 km from rest at one st

1.	A train travels in 3 minutes a distance of 3.15 km from rest at one station to rest at another station. It is uniformly accelerated for the 1st 30 seconds and uniformly retarded for the last 15 seconds, the speed being constant for the remaining time. Find the maximum velocity, acceleration and retardation. Use v-t graph to solve th problem.
Answer» Solution :LET v = maxspeed ATTAINED by the train. From t =0 to t = 30s, acceleration is positive, from t = 30s to t = 165s, acceleration is zero and from t = 165s to t = 180s, acceleration is negative Area under OABC = DISTANCE covered `(1)/(2) (OC+ AB)v = 3150` `(1)/(2) (OC + AB)v = 3150` `rArr v =20m//s` Slope of OA = acceleration in 1ST part ` = v//30 = 2//3 = 0.667 m//s^(2)` Slope of BC = acceleration in IIND part ` = v//15 = -20//15 = 1.334 m//s^(2)`