An automobile rolls down an incline, traveling #s(t) = 6t^2 + 3# feet in #t# seconds. What is the velocity at #t = 2#, and after how many seconds will the velocity be #30# #f##/##sec#?

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Answer 1 · 2015-12-04T16:20:29

#(a)#

#24"ft/s"#

#(b)#

#t=2.5"s"#

(a)

#s(t)=6t^2+3#

To find the velocity at a given instant we need to find the 1st derivative:

#s'(t)=v=12t#

So when #t=2#:

#v=12xx2=24"ft/s"#

(b)

When #v=30#:

#30=12xxt#

#:.t=30/12=2.5"s"#