**Problem Statement:**1. Suppose a car is involved in a collision in which it is brought to a constant speed of 31 m/s. Fortunately, the seat belt worn by the 65 kg driver brought the driver to rest in 0.35 s. How much force is exerted by the seat on the driver? Compute for the acceleration experienced by the driver during collision.**Explanation:**To solve this problem, we need to calculate the force exerted by the seat on the driver and the acceleration experienced by the driver during the collision.**Given Data:**- Initial speed of the car (\(v_i\)) = 31 m/s- Final speed of the driver (\(v_f\)) = 0 m/s (since the driver comes to rest)- Mass of the driver (\(m\)) = 65 kg- Time (\(t\)) = 0.35 s**Calculations:**1. **Acceleration (\(a\)):** Using the formula for acceleration: \[ a = \frac{v_f - v_i}{t} = \frac{0 - 31 \, \text{m/s}}{0.35 \, \text{s}} = \frac{-31}{0.35} \, \text{m/s}^2 \] Calculate \(a\).2. **Force (\(F\)):** Using Newton's second law: \[ F = m \times a \] Substitute the values of \(m\) and \(a\) to find the force. This problem is a practical application of Newton's laws of motion and provides insight into the importance of seat belts in reducing the impact force during collisions.

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1. Suppose a car is involved in a collision in which it is brought to a constant speed of 31 m/s. Fortunately, the seat belt worn by the 65 kg driver brought the driver to rest in 0.35 s. How much force is exerted by the seat on the driver? Compute for the acceleration experienced by the driver during collision.

1. Suppose a car is involved in a collision in which it is brought to a constant speed of 31 m/s. Fortunately, the seat belt worn by the 65 kg driver brought the driver to rest in 0.35 s. How much force is exerted by the seat on the driver? Compute for the acceleration experienced by the driver during collision.

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Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Newton's Second Law

Newton’s laws of motion describe the relationship between the motion of an object and forces acting on it. Newton’s law of motion has two types as follows:

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Question

**Problem Statement:**

1. Suppose a car is involved in a collision in which it is brought to a constant speed of 31 m/s. Fortunately, the seat belt worn by the 65 kg driver brought the driver to rest in 0.35 s. How much force is exerted by the seat on the driver? Compute for the acceleration experienced by the driver during collision.

**Explanation:**

To solve this problem, we need to calculate the force exerted by the seat on the driver and the acceleration experienced by the driver during the collision.

**Given Data:**
- Initial speed of the car (\(v_i\)) = 31 m/s
- Final speed of the driver (\(v_f\)) = 0 m/s (since the driver comes to rest)
- Mass of the driver (\(m\)) = 65 kg
- Time (\(t\)) = 0.35 s

**Calculations:**

1. **Acceleration (\(a\)):**
Using the formula for acceleration:
\[
a = \frac{v_f - v_i}{t} = \frac{0 - 31 \, \text{m/s}}{0.35 \, \text{s}} = \frac{-31}{0.35} \, \text{m/s}^2
\]
Calculate \(a\).

2. **Force (\(F\)):**
Using Newton's second law:
\[
F = m \times a
\]
Substitute the values of \(m\) and \(a\) to find the force.

This problem is a practical application of Newton's laws of motion and provides insight into the importance of seat belts in reducing the impact force during collisions.

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