Intro to Simple Harmonic Motion (Horizontal Springs) Video Lessons

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Problem: An object moves along the x-axis with initial position x(0) =2.  The velocity of the object at time t ≥ 0 is given by .(a) What is the acceleration of the object at time t = 4?(b) What is the total distance traveled by the object over the time interval 0 ≤ t ≤ 4?(c) What is the position of the object at time t = 4?

FREE Expert Solution

We are given a sine/cosine velocity function. Definitely, we realize that this is a motion with calculus problem.

Motion with Calculus:

PVddtdtA

We'll use the above relationship as necessary to answer the questions.

Rules of derivation:

(sin(at))=-1acos(at)+c

ddt(sin(at))=acos(at)

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Problem Details

An object moves along the x-axis with initial position x(0) =2.  The velocity of the object at time t ≥ 0 is given by 

.

(a) What is the acceleration of the object at time t = 4?

(b) What is the total distance traveled by the object over the time interval 0 ≤ t ≤ 4?

(c) What is the position of the object at time t = 4?

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