---
title: "A block of mass m is moving along a horizontal surface with an initial velocity v_0 in the +x-direction. At time t=0, a constant force of magnitude F is applied to the block at an angle ̸ below the horizontal, as shown in the diagram. The force has a horizontal component that opposes the motion of the block. The coefficient of kinetic friction between the block and the surface is μ_k. Which of the following expressions correctly represents the magnitude of the block’s velocity at a later time t, provided the block is still moving in the +x-direction?"
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url: "https://nerd-notes.com/ubq/114615/"
date_modified: "2026-07-03T04:46:26+00:00"
---

# A block of mass m is moving along a horizontal surface with an initial velocity v_0 in the +x-direction. At time t=0, a constant force of magnitude F is applied to the block at an angle ̸ below the horizontal, as shown in the diagram. The force has a horizontal component that opposes the motion of the block. The coefficient of kinetic friction between the block and the surface is μ_k. Which of the following expressions correctly represents the magnitude of the block’s velocity at a later time t, provided the block is still moving in the +x-direction?

A block of mass m is moving along a horizontal surface with an initial velocity v_0 in the +x-direction. At time t=0, a constant force of magnitude F is applied to the block at an angle ̸ below the horizontal, as shown in the diagram. The force has a horizontal component that opposes the motion of the block. The coefficient of kinetic friction between the block and the surface is μ_k. Which of the following expressions correctly represents the magnitude of the block's velocity at a later time t, provided the block is still moving in the +x-direction?

![A square block of mass m rests on a horizontal line representing the ground. A velocity vector v_0 points to the right. An external force vector F originates from the top-center of the block and points diagonally down and to the left. A dashed horizontal line extends to the left from the block's top. The angle ̸ is labeled between this dashed line and the force vector F.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1783053986-Na5BGX.jpg)

- **A.** \( v_0 - \dfrac{t}{m} [F \cos\theta + \mu_k mg] \)
- **B.** \( v_0 - \dfrac{t}{m} [F \cos\theta + \mu_k(mg - F \sin\theta)] \)
- **C.** \( v_0 - \dfrac{t}{m} [F \cos\theta + \mu_k(mg + F \sin\theta)] \)
- **D.** \( v_0 - \dfrac{t}{m} [F \sin\theta + \mu_k(mg + F \cos\theta)] \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/114615/*