Velocity of car v is given by v = at − bt 2 , where a and b are positive constants & t is time elapsed. Find value of time for which velocity is maximum and also corresponding value of velocity?

Question

Velocity of car v is given by v = at − bt 2 , where a and b are positive constants & t is time elapsed. Find value of time for which velocity is maximum and also corresponding value of velocity?

Arun · Answer

Dear Himani V = at - bt&sup2; dV/dt = a - 2bt Put dv/dt = 0 a -2bt = 0 t = a/2b Now d&sup2;v/dt&sup2; is negative at t = a/2b Hence At t = a/2b , velocity will be maximum. Vmax = a * a/2b - b (a/2b)&sup2; = a&sup2;/2b - a&sup2;/4b = a&sup2;/4b

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Velocity of car v is given by v = at − bt 2 , where a and b are positive constants & t is time elapsed. Find value of time for which velocity is maximum and also corresponding value of velocity?

Velocity of car v is given by v = at − bt² , where a and b are positive constants & t is time elapsed. Find value of time for which velocity is maximum and also corresponding value of velocity?

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Velocity of car v is given by v = at − bt 2 , where a and b are positive constants & t is time elapsed. Find value of time for which velocity is maximum and also corresponding value of velocity?

Velocity of car v is given by v = at − bt2 , where a and b are positive constants & t is time elapsed. Find value of time for which velocity is maximum and also corresponding value of velocity?

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Velocity of car v is given by v = at − bt² , where a and b are positive constants & t is time elapsed. Find value of time for which velocity is maximum and also corresponding value of velocity?