Object traveled

Question

For an object whose velocity in ft/sec is given by v(t) = -2t^2 + 8, what is its distance travelled, in feet, on the interval t = 0 to t = 3 secs?

6.00

0.67

15.33

5.11

 

 

Answer 1

Jay,

The integral of velocity is distance, so we need to integrate the function [v(t)] given over the interval 0 to 3.

∫₀³ -2t²+8 dt = -2t³/3 + 8t |30

-2(3³)/3 + 8(3) - [-2(0³)/3 + 8(0)] = -18 + 24 = 6

The object travels 6 ft during the interval from 0-3 seconds.