Newton's Second Law — Question 2

Question 2

Opposite force and velocity describe slowing before reversal

Use $\sum\vec F=m\vec a$ for constant mass in an inertial frame. A 3 kg body initially moves east at 8 m/s. A constant net force of 6 N west acts for 6 s.

1. Find when it stops momentarily.

2. Find its final velocity and displacement.

3. Find total distance and identify when its speed increases.

Question 2 - Solution

Opposite force and velocity describe slowing before reversal

(a) Keep east positive.

$$a=-6/3=-2,\quad0=8-2t_*\ \Rightarrow\ \boxed{t_*=4\,\mathrm s}$$ $a=-6/3=-2$ m/s$^2$ and $v=8-2t$ m/s. It stops at t=4 s.

(b) Continue beyond the zero of velocity.

$$v(6)=8-12=-4\,\mathrm{m/s},\quad\Delta x=8(6)-6^2=12\,\mathrm m$$ At 6 s, $v=-4$ m/s. Displacement is $8(6)-6^2=12$ m east.

(c) Split the distance at reversal.

$$x(4)=16\,\mathrm m,\quad s=|16|+|12-16|=20\,\mathrm m,\quad\frac{d|v|}{dt}=a\,\mathrm{sgn}(v)$$ It travels 16 m east before stopping, then 4 m west, for total distance 20 m. Speed decreases for $0<t<4$ and increases for $4<t<6$. A westward net force does not imply westward motion throughout.