A subway train travels between two of its station stops with the acceleration schedule shown. Determine the time interval Δ t during which the train brakes to a stop with a deceleration of 2m/s 2 and find distance ‘s’ between stations.
Text Solution
Verified by ExpertsSol. Area under graph gives change in velocity
Train starts from rest and comes to rest
Therefore,
Positive area = negative area
8 × 1 + 6 × 2 = 2 × Δ t
8 + 12 = 2 Δ t
Δ t = 
= 10sec .
Displacement & distance are equal in this case displacement can be directly calculated from at curve without using v-t curve as follows
Δ S = ut 0 + (area under a-t curve) (t 0 – t c )
Where u → initial velocity
t 0 → total time
t c → abscissa of centroid of corresponding area
Δ s = 8 [34 – 4] + 12 [34–11] + (–20) [34–29]
= 8 × 30 + 12 × 23 – 20 × 5
= 240 + 276 – 100
= 516 – 100
Δ s = 416m.
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