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The concept of deceleration is crucial when analyzing situations where an object is slowing down, as in the case of a car crash. Deceleration, which can be understood as negative acceleration, is the rate at which the velocity of an object decreases. To calculate deceleration, the change in velocity \( \Delta v \) is divided by the time \( t \) in which this change occurs. Specifically, for our exercise where a car halts from an initial velocity of \(10 \text{ m/s}\) to a standstill, the formula is:
\[ a = \frac{\Delta v}{t} \]
To compute the deceleration value, we must acknowledge that the change in velocity is \( -10 \text{ m/s} \) as the car goes from \(10 \text{ m/s}\) to \(0 \text{ m/s}\), and the time taken to stop is \(0.26 \text{ s}\). Therefore, the deceleration calculation yields a magnitude of \( -38.46 \text{ m/s}^2 \) showing a quick and significant decrease in speed in a very short time.

Newton's second law of motion serves as a foundation for understanding the forces involved when an object's motion changes, as seen with the decelerating passenger in a car crash. This law states that the force applied on an object is equal to the mass of the object multiplied by its acceleration \( F = ma \).
In our problem, 'acceleration' refers to the deceleration since it's the type of acceleration experienced by the passenger when the car stops abruptly. To find out the amount of force exerted, it's essential to use the mass of the passenger and their calculated deceleration. Remember, force is a vector quantity, which means it has both a magnitude and a direction. The direction of the force is opposite to the direction of deceleration indicating that it acts to stop the passenger, adhering to Newton's principle for the force equation applied in real-world scenarios.

The final step in our physics problem involves calculating the force exertion. When a seat belt halts a passenger abruptly, it exerts a force to counteract the motion due to the car crash. By multiplying the mass of the passenger \(70 \text{ kg}\) by the deceleration \( -38.46 \text{ m/s}^2 \), you attain the force exerted by the seat belt. It is worth noting here that the negative sign indicates the direction of the force.
In the real world, the seat belt's force is in the opposite direction to the passenger’s inertia (the tendency of the passenger to maintain its uniform motion), thereby ensuring their safety by bringing them to a stop. A thorough understanding of force exertion through the lens of Newton's laws allows us to design safer vehicles and develop better safety mechanisms that protect passengers during collisions.