Height attained by particle in vertical direction changing with time #y= 5t-5t^2# then maximum height attained by particle is?

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Answer 1 · 2017-03-12T11:18:10

The maximum height is #=1.25m#

We determine the first and second derivatives

#y=5t-5t^2#

#dy/dt=5-10t#

#dy/dt=0# when #5-10t=0#

That is,

#5=10t#

#t=1/2#

#(d^2y)/dt^2=-10#

As, #(d^2y)/dt^2<0#, this is a maximum

#y(2)=5*1/2-5*1/4=5/4=1.25m#

graph{5x-5x^2 [-3.442, 3.486, -0.016, 3.448]}