Math Problem Statement

A 2450 kg car slows down at a rate of 3.5 m/s² when approaching a stop sign. What is the magnitude of the net force causing it to slow down?

Solution

The problem in the image asks:

A 2450 kg car slows down at a rate of 3.5 m/s² when approaching a stop sign. What is the magnitude of the net force causing it to slow down?

To find the magnitude of the net force, we can use Newton's Second Law of Motion, which states:

F=maF = ma

Where:

  • FF is the net force,
  • mm is the mass of the car (2450 kg),
  • aa is the acceleration (here it's a deceleration of 3.5m/s23.5 \, \text{m/s}^2).

Let's calculate the force:

F=2450kg×3.5m/s2=8575NF = 2450 \, \text{kg} \times 3.5 \, \text{m/s}^2 = 8575 \, \text{N}

So, the magnitude of the net force is 8575 N (Newtons).

Would you like further details or explanations on how this was solved? Here are 5 related questions to deepen your understanding:

  1. What happens to the force if the mass of the car increases?
  2. How would the force change if the car decelerates faster, say at 5m/s25 \, \text{m/s}^2?
  3. What other factors, besides mass and acceleration, could affect the net force?
  4. What is the difference between force and weight in this context?
  5. How is net force related to velocity?

Tip: Remember, net force always acts in the direction of acceleration (or deceleration, as in this case), whether speeding up or slowing down.

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Math Problem Analysis

Mathematical Concepts

Physics
Newton's Second Law of Motion
Force
Deceleration

Formulas

F = ma

Theorems

Newton's Second Law

Suitable Grade Level

Grades 9-12