Question

an automobile can accelerate Audi accelerate at a maximum value of 5/3 m/sec² and can attend a maximum speed of 90 km/hr. if it starts from rest, what is the shortest time in which can travel one km, if it is to come to rest at the end of the kilometre Run?

Answer 1

$solution$
in order that the time of motion be shortest, the car should attend the maximum velocity with the maximum acceleration after the start, maintain the maximum velocity for as long as possible and then the decelerate with the maximum retardation possible, consistent with the condition that, the automobile should come to rest immediately after covering a distance of one km.

Let t1 be the time of acceleration, t2 be the time of uniform velocity and t3 be the time of retardation.

NOW ,

maximum velocity possible = 90 km/hr

= 90 * 5/18 m/sec

= 25 m/sec


t1 = v-u/a = 25 - 0 /5/3

= 25 * 3 /5

= 15 second

similarly,

during retardation

t3 = 0-25/-5/3 = 15 second


✨ during the period of acceleration, the distance covered = average velocity * time = 25 + 0/2 * 15

= 187.5 m

✨ during the period of the acceleration, the distance covered is the same hence

= 187.5m

✨ the total distance covered under constant velocity = 1000- 375

= 625 m

✨ time of motion under constant velocity t2 = 625/25

= 25 second

✨ the shortest time of motion = t1 + t2 + t3

= 15 + 25 + 15

= 55 seconds.

__________________________
❤BE BRAINLY ❤

Answer 2

Answer:

55sec.

Explanation:

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