An object moves along a coordinate line with acceleration a(t)=t^3+9t^2+27t+27 units per second per second. The initial velocity is 22 units per second. The velocity function is v(t)=

Question

An object moves along a coordinate line with acceleration a(t)=t^3+9t^2+27t+27 units per second per second.

The initial velocity is 22 units per second.

The velocity function is v(t)=

The initial position is 77 units to the right of the origin.

The position function is s(t)=

Answer 1

v(t) = ∫(t³ + 9t² + 27t + 27)dt = t⁴/4 + 3t³ + 27/2t² + 27t + C₁; v(0) = C₁ = 22; v(t) = t⁴/4 + 3t³ + 27/2t² + 27t + 22;

s(t) = ∫(t⁴/4 + 3t³ + 27/2t² + 27t + 22)dt = t⁵/20 + 3t⁴/4 + 9/2t³ + 27/2t² + 22t + C₂; s(0) = C₂ = 77;

s(t) = t⁵/20 + 3t⁴/4 + 9/2t³ + 27/2t² + 22t + 77.