Math Problem Statement

The graph shows velocity versus time for a 2.0 kg sled pulled on a level surface by a constant horizontal force. What is the net horizontal force acting on the sled?

Solution

To solve this problem, let's analyze the given data and apply Newton's second law of motion.

Given Information:

  • Mass of the sled (m): 2.0 kg
  • Velocity vs. Time Graph: Shows a linear increase in velocity, indicating a constant acceleration.
  • Objective: Determine the net horizontal force acting on the sled.

Step-by-Step Solution:

  1. Determine the Acceleration from the Graph:

    • Since the velocity vs. time graph is linear, we can calculate the acceleration using the slope of the line.
    • The graph shows an increase in velocity from 0m/s0 \, \text{m/s} to 10m/s10 \, \text{m/s} over 8s8 \, \text{s}.
    • Acceleration (a) is given by: a=ΔvΔt=10m/s0m/s8s=1.25m/s2a = \frac{\Delta v}{\Delta t} = \frac{10 \, \text{m/s} - 0 \, \text{m/s}}{8 \, \text{s}} = 1.25 \, \text{m/s}^2
  2. Apply Newton’s Second Law:

    • Newton's second law states that the net force FF acting on an object is given by F=maF = m \cdot a.
    • Substituting the values: F=2.0kg×1.25m/s2=2.5NF = 2.0 \, \text{kg} \times 1.25 \, \text{m/s}^2 = 2.5 \, \text{N}
  3. Compare with Options:

    • The calculated net force F=2.5NF = 2.5 \, \text{N} is closest to none of the given options directly, but it suggests that this is a calculation problem. If we confirm with exact slope

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Math Problem Analysis

Mathematical Concepts

Physics
Kinematics
Newton's Laws of Motion

Formulas

a = Δv / Δt
F = m * a

Theorems

Newton's Second Law of Motion

Suitable Grade Level

Grades 9-12