Free ResponseThe position of an object moving along a line at any time t > 0 is given by the functions(t) = t3 – 9t² + 18 , where s is measured in feet and t is measured in seconds.A) Find the velocity of the particle at t = 4.B) Find the acceleration of the particle at t = 4.C) Was the speed of the particle increasing or decreasing at t = 4 ? Justify your answer.D) For t > 0, find the acceleration when the particle changes direction.

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Description: Free ResponseThe position of an object moving along a line at any time t > 0 is given by the functions(t) = t3 – 9t² + 18 , where s is measured in feet and t is measured in seconds.A) Find the velocity of the particle at t = 4.B) Find the accelerati

The position of an object is given by,s(t)=t3-9t2+18........ t≥0......(1)where, s(t) is in feets…

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The position of an object moving along a line at any time t 2 0 is given by the function s(t) = t³ – 9t² + 18 , where s is measured in feet and t is measured in seconds.

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Concept explainers

Displacement, Velocity and Acceleration

In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.

Linear Displacement

The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.

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The position of an object moving along a line at any time t > 0 is given by the function
s(t) = t3 – 9t² + 18 , where s is measured in feet and t is measured in seconds.
A) Find the velocity of the particle at t = 4.
B) Find the acceleration of the particle at t = 4.
C) Was the speed of the particle increasing or decreasing at t = 4 ? Justify your answer.
D) For t > 0, find the acceleration when the particle changes direction.

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