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An object moves along a coordinate line with velocity v(t) = t(7-t) units per se

ID: 2842094 • Letter: A

Question

An object moves along a coordinate line with velocity v(t) = t(7-t) units per second.

Its initial position is 5 units to the left of the origin.

(a) Find the position of the object 13 seconds later.

ANSWER: The new position is_____units to the right of the origin.

  Note: If the object is positioned to the left of the origin at t = 13 seconds,

  then your answer above will be negative.


(b) Find the total distance traveled by the object during those 13 seconds.


  ANSWER: The object traveled a total distance of_______ units.

Explanation / Answer

a(t) = 0.5(t+1)^3 units per second per second
v = 0.125 (t + 1)^4 + C, when t = 0, v = 4 hence C = 32 hence v(t) = 0.125(t + 1)^4 + 32
s = 0.025(t + 1)^5 + 32t + C, when t = 0, s = 0 hence C = -- 0.025
s(t) = 0.025 [(t + 1)^5 -- 1] + 32t