What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) = 16-t^2# from #t in [0, 4]#?

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Answer 1 · 2016-04-28T13:08:32

#26 2/3#

given,

#a(t) = 16-t^2#

#=> v(t) = int_o^t(16-t^2)dt = 16t-1/3t^3, # as #v(0) = 0;#

#"avg. speed" = (int_o^4(16t-1/3t^3)dt)/(int_0^4dt) = 1/4(8[t^2]_0^4-1/12 [t^4]_0^4) = (32-16/3) = 26 2/3#