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Question

#16t^2

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Answer 1 · 2017-09-03T20:05:24

(a) #80# #"ft/sec"#
(b) #160# #"ft/sec"#

Average speed is given by:

#barv=(Deltax)/(Deltat)#

Here, #Deltax# is the change in position, or #s(5)-s(0)# feet.
#Deltat# is #5-0# seconds.

#barv=(s(5)-s(0))/(5-0)# #"ft/sec"#

#color(white)barv=(16*25-16*0)/5# #"ft/sec"#

#color(white)barv=80# #"ft/sec"#

To find the instantaneous velocity at #t=5#, we need to differentiate #s# to find #v#.

#v=(ds)/dt=d/dt16t^2=32t#

Thus, at #t=5#:

#v=32*5=160# #"ft/sec"#