Newton's First Law — Question 1

Question 1

Coasting does not require a forward net force

A puck moves at 3 m/s east on an ideal horizontal surface. At t=0 the brief push ends. All remaining forces balance. Treat the ground as inertial.

1. Find its velocity and displacement over the next 4 s.

2. Does the end of the push make it gradually stop in this model?

3. If a real puck slows, what assumption needs revision?

Question 1 - Solution

Coasting does not require a forward net force

(a) Apply zero net force to velocity.

$$\sum\vec F=\vec0\ \Rightarrow\ \vec a=\vec0,\quad \boxed{v_x=3\,\mathrm{m/s},\quad\Delta x=3(4)=12\,\mathrm m}$$ The first law gives constant velocity, 3 m/s east. Displacement in 4 s is 12 m east.

(b) Do not confuse force with velocity.

$$v_x(t)=v_x(0)+\int_0^t0\,du=v_x(0)$$ No forward net force is needed to maintain the existing velocity. The stipulated model contains no unbalanced interaction that could change it.

(c) Reopen the interaction inventory.

$$\frac{dv_x}{dt}<0\ (v_x>0)\ \Rightarrow\ F_{{\mathrm{net}},x}=m\frac{dv_x}{dt}<0$$ Slowing would require nonzero acceleration and thus failure of the balanced-force assumption in an inertial frame. Surface resistance or air interaction could explain it. That physical evidence revises the idealization, not the first law itself.