For an object whose velocity in ft/sec is given by v(t) = −t2 + 4, what is its displacement, in feet, on the interval t = 0 to t = 3 secs?

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Answer 1 · 2018-03-14T14:56:54

#3# feet.

So we have that #v(t)=-t^2+4#.

We are required to find #s(t)#, where #v(t)=s'(t)#, on the interval #[0,3]#. We can do this using:

#int_0^3(-t^2+4) dt#

Calculating the indefinite integral:

#-1(intt^2dt-int4dt)#

#-1(t^3/3-4t)#

#-t^3/3+4t+C#

When the integral is definite, the constants cancel out, and adding the bounds in:

#[-t^3/3+4t]_0^3#

Since inputting #0# won't affect anything, we can just input #3#:

#-3^3/3+3(4)#

#-27/3+12#

#-9+12#

#3 quad "ft"#

So the particle has a displacement of #3# feet.