The velocity function (in meters per second) is given for a particle moving alon

Question

The velocity function (in meters per second) is given for a particle moving along a line.

Explanation / Answer

integrate v(t) to get d(t). So, d(t) = (3/2)t^2 - 8t. (a) (3/2)(3)^2 - 8(3) - (3/2)0^2 - 8(0) = -10.5 meters. (b) set v(t) = 0, solve for t. 0 =3t-8. ==> t=(8/3) Now the object is traveling backwards from time 0 to 8/3 then switches direction and travels forward from 8/3 until 4. Therefore we want to integrate each interval separately, take the absolute value of each, then add them together to get the total distance traveled. (3/2)(8/3)^2 - 8(8/3) = (-32/3) or | (-32/3) | = 32/3 =10.66 (3/2)(3)^2 - 8(3) - (3/2)(8/3)^2 + 8(8/3) = 0.163 Add together and you get 10.832 total meters traveled.

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