The velocity function (in meters per second) for a particle moving along a line is given by v(t)=t^3–4t^2?
The velocity function (in meters per second) for a particle moving along a line is given by v(t)=t^3–4t^2. Find the displacement and the distance traveled by the particle during the time interval [-1,5]. (Hint: Draw a graph of the velocity function.) Your answers require that you enter the correct units.
Displacement = __________
Distance traveled = __________
10pts for answering!
More Questions From This User See All
Answers & Comments
Verified answer
displacement = s{ t } = ∫ v{ t } dt
5
s{5} – s{-1} = ∫ (t³ – 4t²) dt = (5^4) ⁄ 4 – (4 • 5³ ⁄ 3) – [ (-1)^4 ⁄ 4 – (4(-1)³ ⁄ 3) ]
-1
= (625 ⁄ 4) – (500 ⁄ 3) – (1 ⁄ 4) – (4 ⁄ 3)
= -12 meters ... displacement