Answered: a) displacement and distance traveled…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter2: Motion In One Dimension

Section: Chapter Questions

Problem 10P: An object moves along the x axis according to the equation x = 3.00t2 2.00t + 3.00, where x is in...

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Question

The equation

x(t) = −bt² + ct³

gives the position of a particle traveling along the x axis at any time. In this expression,

b = 6.00 m/s²,

c = 4.00 m/s³,

and x is in meters when t is entered in seconds. For this particle, determine the following. (Indicate the direction with the sign of your answer as applicable.)

(a) displacement and distance traveled during the time interval

t = 0

t = 3 s

(Enter your answers to at least two decimal places.)

(b) average velocity and average speed during the time interval

t = 0

t = 3 s

(Enter your answers to at least two decimal places.)

(c) average acceleration during the time interval

t = 0

t = 3 s

Expert Solution

Step 1

Particle’s position at t= 0s,

Here, t represents the time.

Substitute the relevant values.

Particle’s position at t= 3s,

Substitute the relevant values.

The particle’s displacement can be represented as,

Substitute the relevant values.

Now, let us find the turning point of the particle,

Substitute the relevant values.

Thus, the particle changes direction at t = 1s.

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