A shopping cart is pushed with a constant horizontal force of 5 N, with negligible friction and balanced vertical forces. Describe the cart’s motion (direction, whether speed/velocity are constant or changing, and whether acceleration exists).

What you should decide from the force information

Motion comes from the net force. If the net force is zero, velocity stays constant. If the net force is not zero, the object accelerates, meaning its velocity changes.

Forces on the cart: vertical vs. horizontal

• Vertical forces are balanced (normal force up equals weight down), so the net vertical force is $0$. That means no vertical acceleration and the cart stays on the floor.
• Friction is negligible, and you apply a constant horizontal push of $5\,\text{N}$, so the net horizontal force is $$F_{\text{net}, x}=5\,\text{N}.$$

What Newton’s 2nd law says about the motion

Newton’s 2nd law gives $$a_x=\frac{F_{\text{net}, x}}{m}=\frac{5}{m}.$$ Since $5\,\text{N}$ is constant and the cart’s mass $m$ is constant, $a_x$ is constant.

Complete motion description (what happens to speed, velocity, direction)

• Direction of travel: along the direction you push (straight ahead).
• Acceleration: yes, constant and forward, with magnitude $5/m$.
• Speed: not constant, it increases at a constant rate. If the cart starts from rest, $v(t)=\frac{5}{m}t$.
• Velocity: not constant because its magnitude increases; its direction stays the same (straight line), assuming you keep pushing in the same direction.

What the position does (optional but completes the picture)

With constant acceleration, position changes like $$x(t)=x_0+v_0 t+\tfrac{1}{2}\left(\frac{5}{m}\right)t^2,$$ so the cart’s distance traveled grows faster and faster as time goes on.