   Chapter 2.3, Problem 63E

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# The equation of motion of a particle is s = t 3 − 3 t , where s is in meters and t is in seconds. Find(a) the velocity and acceleration as functions of t,(b) the acceleration after 2 s, and(c) the acceleration when the velocity is 0.

To determine

To find:

(a) The velocity and acceleration as functions of t

(b) The acceleration after 2 s

(c) The acceleration when the velocity is 0

Explanation

Formula:

velocity=dsdt

acceleration=dvdt

where s(t) is displacement as a function of time.

Constant function rule: d(C)dx=0

Power function rule: d(xn)dx=nxn-1

Constant multiple rule: d(Cf(x))dx=Cd(f(x))dx

Difference rule: d(fx-g(x))dx=d(f(x))dx-d(g(x))dx

Given:

The equation of motion of particle is s=t3-3t

Calculation:

(a)

velocity=v= dsdt=d(t3-3t)dt

By difference rule,

v=d(t3)dt-d(3t)dt

By power function rule and constant multiple rule,

v=3t2-3d(t)dt

=3t2-3

Therefore, velocity=3t2-3 m/s

a

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