Question

begins A commuter train traveling at 45MPH is ómiles from the station. The train to decelerate so that its speed is 15MPH when it is 0.5miles from the station. Knowing that the train arrives at the station 14minutes after beginning to decelerate and assuming constant deceleration, find : a) time required for the train to travel the first 5.5 miles, b) the final deceleration of the train, c) the speed of the train as it arrives at the station.

Answer 1

initial speed of train = 45 mph = 20.11 m/s

distance of train from station = 6 miles = 9656 m

final speed of train = 15 mph = 6.706 m/s

distance of train from station = 0.5 miles=804.67 m

distance travelled = 9656-804.67 = 8851.39 m

let deceleration be a

6.706² = 20.11²+(2*a*8851.39)

a=-0.02 m/s²

deceleration = 0.02 m/s²

let time required be t

t=(20.11-6.706)/0.02=670.2 seconds

let final deceleration be a

0²=6.706²+2*a*804.67

a=-0.028 m/s²

final deceleration = 0.028 m/s²