Question

A 5.8kg object, initially at rest, is acted on by a net external force in a straight line described by F=8(1-exp(-0.2t))N, where t is in seconds.

a) What is the magnitude of the momentum of the object after 11.5s have elapsed?

b) What is the work of the net external force after 11.5s have elapsed?

Answer 1

\[ F = 8(1-e^{-0.2t})N\]

\[ \frac{d \textbf p}{dt} = \textbf F\]
\[ \int_{p_o}^{p} d\textbf p = \int_{t_i}^{t_f}\textbf F dt\]
\[ p_{t=11.5s} = \int_{0}^{11.5s}8(1-e^{-0.2t})Ndt\]

2) what is the work done by the net external force?
Work enrgy principle:
\[ W = \Delta K \]
K is kinetic energy
\[ K = \frac{1}{2}mv^2 \]

:)