Object Velocity

Question

For an object whose velocity in ft/sec is given by v(t) = -t^2 + 6, what is its displacement, in feet, on the interval t = 0 to t = 6 secs?

-36

36

0

55.596

Answer 1

Linda.

 

We need to integrate this function over the interval 0-6 seconds.

 

∫₀⁶ -t²+6 dt

 

-t³/3 + 6t  |⁶₀

 

-(6³)/3 + 6(6) - [-(0³)/3 + 6(0)]

-216/3 + 36 - 0

-72+36 = -36

 

Over a 6 second interval, this object will be displaced by -36 feet.