A particle of mass m is located at the origin. It is at rest and in equilibrium. A time-dependent force of F(t) is applied at time t = 0, and its components are F(t) = pt' and F,(t) = n + qt where p, q, and n are constants. Find the position r(t) and velocity v(t) as functions of time t. (Express your answers in vector form with exact values. Use the following as necessary: m, p, q, n, and t.) r(t) = v(t) = i+ 8m nt +

A particle of mass m is located at the origin. It is at rest and in equilibrium. A time-dependent force of F(t) is applied at time t = 0, and its components are F(t) = pt' and F,(t) = n + qt where p, q, and n are constants. Find the position r(t) and velocity v(t) as functions of time t. (Express your answers in vector form with exact values. Use the following as necessary: m, p, q, n, and t.) r(t) = v(t) = i+ 8m nt +

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A helicopter with mass \(2.95 \times 10^4\) kg has a position given by \(\vec{r}(t) = (0.030t^3\hat{\imath} + 3.3t\hat{\jmath} - 0.070t^2\hat{k})\) m. Find the net force on the helicopter at \(t = 3.0\) s. (Express your answer in vector form. Assume that \(\vec{F}\) is in newtons when \(t\) is in seconds. Do not include units in your answer.)

\[
\vec{F}(3.0 \, \text{s}) = \boxed{\phantom{000}} \, \text{N}
\]

A particle of mass \( m \) is located at the origin. It is at rest and in equilibrium. A time-dependent force of \( \vec{F}(t) \) is applied at time \( t = 0 \), and its components are \( F_x(t) = pt^7 \) and \( F_y(t) = n + qt^3 \) where \( p, q, n \) are constants. Find the position \( \vec{r}(t) \) and velocity \( \vec{v}(t) \) as functions of time \( t \). (Express your answers in vector form with exact values. Use the following as necessary: \( m, p, q, n, \) and \( t \).)

\[ \vec{r}(t) = \]

\[ \vec{v}(t) = \left( \frac{pt^8}{8m} \right) \hat{i} + \frac{1}{m} \left( nt + \frac{qt^4}{4} \right) \hat{j} \]

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