An object moves along a coordinate line with acceleration $a(t) = (t + 5)^3$ units per second per second. The initial velocity is 9 units per second. The velocity function is $v(t) =$ The initial position is 7 units to the right of the origin. The position function is $s(t) = $
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Since acceleration is the derivative of velocity with respect to time, we can find v(t) by integrating a(t) with respect to t: v(t) = ∫(t + 5)^3 dt Now, we can use the power rule for integration: v(t) = (1/4)(t + 5)^4 + C We are given that the initial velocity Show more…
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