Position, Velocity, and Acceleration values from Position Function| University Physics

ANSWER: 42.0 m

Evaluate the position at time t= 3.00 s.

$\displaystyle x=2.00\left(3\right)^3-5.00\left(3\right)+3=42.0\:m$

ANSWER: 49.0 m/s

Determine the velocity function v(t) from the position function x(t) by differentiation.

$\displaystyle v\left(t\right)=6t^2-5$

$\displaystyle v\left(t\right)=6\left(3\right)^2-5=49.0\:m/s$

ANSWER: 36.0 m/s²

Determine the acceleration function a(t) from the the velocity function by differentiation

$\displaystyle a\left(t\right)=12t$

$\displaystyle a\left(t\right)=12t=12\left(3\right)=36\:m/s^2$

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