---
title: "Four different one-dimensional forces act on identical blocks, each initially at rest on a frictionless horizontal surface, over the time interval \\(0 \\le t \\le T\\).  The functional form of each force is given in the table, where \\(F_0\\) and \\(T\\) are positive constants.  | Force Profile | Functional Form | | :— | :— | | Profile 1 | \\(F_1(t) = F_0 \\sin\\left(\\dfrac{\\pi t}{T}\\right)\\) | | Profile 2 | \\(F_2(t) = F_0 \\left(\\dfrac{t}{T}\\right)\\) | | Profile 3 | \\(F_3(t) = 4F_0 \\left(\\dfrac{t}{T}\\right)\\left(1 – \\dfrac{t}{T}\\right)\\) | | Profile 4 | \\(F_4(t) = F_0 \\left(\\dfrac{t}{T}\\right)^2\\) |  Which of the following correctly ranks the magnitude of the impulse \\(J\\) delivered to each block by its respective force during the interval from \\(t = 0\\) to \\(t = T\\)?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/123988/"
date_modified: "2026-09-28T13:29:59+00:00"
---

# Four different one-dimensional forces act on identical blocks, each initially at rest on a frictionless horizontal surface, over the time interval \(0 \le t \le T\).

The functional form of each force is given in the table, where \(F_0\) and \(T\) are positive constants.

| Force Profile | Functional Form |
| :— | :— |
| Profile 1 | \(F_1(t) = F_0 \sin\left(\dfrac{\pi t}{T}\right)\) |
| Profile 2 | \(F_2(t) = F_0 \left(\dfrac{t}{T}\right)\) |
| Profile 3 | \(F_3(t) = 4F_0 \left(\dfrac{t}{T}\right)\left(1 – \dfrac{t}{T}\right)\) |
| Profile 4 | \(F_4(t) = F_0 \left(\dfrac{t}{T}\right)^2\) |

Which of the following correctly ranks the magnitude of the impulse \(J\) delivered to each block by its respective force during the interval from \(t = 0\) to \(t = T\)?

Four different one-dimensional forces act on identical blocks, each initially at rest on a frictionless horizontal surface, over the time interval \(0 \le t \le T\).

The functional form of each force is given in the table, where \(F_0\) and \(T\) are positive constants.

| Force Profile | Functional Form |
| :--- | :--- |
| Profile 1 | \(F_1(t) = F_0 \sin\left(\dfrac{\pi t}{T}\right)\) |
| Profile 2 | \(F_2(t) = F_0 \left(\dfrac{t}{T}\right)\) |
| Profile 3 | \(F_3(t) = 4F_0 \left(\dfrac{t}{T}\right)\left(1 - \dfrac{t}{T}\right)\) |
| Profile 4 | \(F_4(t) = F_0 \left(\dfrac{t}{T}\right)^2\) |

Which of the following correctly ranks the magnitude of the impulse \(J\) delivered to each block by its respective force during the interval from \(t = 0\) to \(t = T\)?

- **A.** \(J_3 > J_1 > J_2 > J_4\)
- **B.** \(J_1 > J_3 > J_2 > J_4\)
- **C.** \(J_3 > J_2 > J_4 > J_1\)
- **D.** \(J_4 > J_2 > J_3 > J_1\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123988/*