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

Problem:

A particle moving along the x-axis has its position described by the function x=\left(2.00t^3-5.00t+3.00\right)m, where t is in s. At t= 3.00, what are the particle’s (a) position, (b) velocity, and (c) acceleration?

PART A.

ANSWER: 42.0 m

Evaluate the position at time t= 3.00 s.

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

PART B.

ANSWER: 49.0 m/s

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

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

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

PART C.

ANSWER: 36.0 m/s²

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

a\left(t\right)=12t

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

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