Does it take longer to accelerate from 0-50mph or from50-100mph? If it took 5 se

Question

Does it take longer to accelerate from 0-50mph or from50-100mph? If it took 5 seconds to accelerate from 0-50mph and used 1gallon of gas is it right to assume that it will only take oneadditional gallon to go from 50-100mph and that it too will onlytake 5 seconds?
This is just something my friends and I were discussing. Somesay that since the car is already moving it will take less time forit to make the next speed gap and it will use less gas and otherssaid that they heard on top gear that it takes twice as much energyto accelerate to twice the current speed which lead them to thinkthat it would use twice the amount of gas but it would take thesame amount of time.
I am party to the second camp. Twice the gas, same amount oftime. Answer the sooner the better I suppose. If it took 5 seconds to accelerate from 0-50mph and used 1gallon of gas is it right to assume that it will only take oneadditional gallon to go from 50-100mph and that it too will onlytake 5 seconds?
This is just something my friends and I were discussing. Somesay that since the car is already moving it will take less time forit to make the next speed gap and it will use less gas and otherssaid that they heard on top gear that it takes twice as much energyto accelerate to twice the current speed which lead them to thinkthat it would use twice the amount of gas but it would take thesame amount of time.
I am party to the second camp. Twice the gas, same amount oftime. Answer the sooner the better I suppose.

Explanation / Answer

   First equation gives timeas      t   =   (v- u) / a    v   =   finalspeed,   u   =   initialspeed,   a   =   acceleration    Assuming acceleration to be constant, thedifference (v - u) is same which means that the time taken will besame for 0 - 50 mph and 50 - 100 mph.    Initialenergy   K1   =   0      (Caris at rest)    energy at 50mph   =   (1/2) * m *v12                                  =   0.5* m * 502                                  =   1250* m    K.E.gained   K1   =   1250* m      units    energy at 100mph   =   0.5 * m * 1002                                  =   5000* m    K.E.gained   K2   =   5000* m   -   1250 * m                                  =   3750* m   units    Since energy gained in from 50 mph - 100 mphis 3 times energy gained from 0 - 50 mph, three times gas ( not twice) gaswill be consumed.                                  =   5000* m    K.E.gained   K2   =   5000* m   -   1250 * m                                  =   3750* m   units    Since energy gained in from 50 mph - 100 mphis 3 times energy gained from 0 - 50 mph, three times gas ( not twice) gaswill be consumed.

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