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Find the total distance travelled in minimum time taken by car that starts from rest and comes to rest after achieying a peak velocity of 16m/s while moving along a straight line.The magnitude of maximum acceleration and maximum retardation is same at 2m/s^(2).
Asked by anurajdas516 | 27 Dec, 2021, 02:01: PM
To get minimum time, acceleration and retardation should be maxiuossible .

Hence we consider acceleration and retrdation as 2 m/s2

Distance S1 travelled while acceleration is determined form the following equation of motion

" v2 = u2 + ( 2 a S1 )  "

where v is velocity attained after travelling a distance S1 with accleration a .

u is initial velocity that is zero because car starts from rest

S1 = v2 / ( 2 a )  =  256 / 4 = 64 m

Distance S2 travelled while acceleration is determined form the following equation of motion

" v2 = u2 - ( 2 a S2 )  "

where v is final velocity after travelling a distance S2 with retardation a .

v is zero because the car comes to rest after travelling distance S2

u = 16 m,/s  is initial velocity

S2 = u2 / ( 2 a )  =  256 / 4 = 64 m

Total distance travelled = S1 + S2 = 128 m

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