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Grade 12Trigonometry

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?

Profile image of himani
8 Years agoGrade 12
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1 Answer

Profile image of Arun
ApprovedApproved Tutor Answer8 Years ago
Dear Himani
 
V = at - bt²
dV/dt = a - 2bt
Put dv/dt = 0
a -2bt = 0
t = a/2b
Now d²v/dt² is negative at t = a/2b
Hence
At t = a/2b , velocity will be maximum.
Vmax =  a * a/2b - b (a/2b)² = a²/2b  -  a²/4b = a²/4b

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