{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PS1-5

PS1-5 - Problem Set 1 Problem 5 Problem The acceleration of...

This preview shows pages 1–2. Sign up to view the full content.

Problem Set 1: Problem 5. Problem: The acceleration of a particle is a = kt , where k is a constant to be determined. Its position and velocity at t = 0 are x (0) = 0 and v (0) = v o , respectively, where v o > 0 . The particle’s velocity at time t = τ is v ( τ ) = 8 9 v o . (a) Determine the constant k as a function of v o and τ . Based on your solution for k , express the velocity as a function of t , τ and v o . (b) Solve for the particle’s position as a function of t , τ and v o . (c) What is the total distance traveled by the particle from t = 0 to t = 9 τ ? NOTE: Be sure to account for the fact that the particle changes direction during this time interval. Solution: Since we know the velocity at two different times, the obvious first step in solving this problem is to integrate the acceleration over time to determine the velocity. That will yield sufficient information to determine k . (a) The velocity is given by v ( t ) = 8 t 0 kt dt = v o + 1 2 kt 2 Now, we make use of the fact that v ( τ ) = 8 9 v o , i.e., v o + 1 2 k τ 2 = 8 9 v o Solving for k yields k =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern