91Ó°ÊÓ

Deceleration is simply acceleration in the opposite direction. An object slows down when the net force acting on it is opposite to its direction of travel. In the given problem, the car's speed decreases from an initial value to a lower final value over a certain period. This means the car is decelerating. To calculate deceleration, you subtract the final velocity from the initial velocity and then divide by the time span. This negative acceleration indicates slowing down.
The formula used is:

• Initial velocity (\(v_i = 27.0 \text{ m/s}\))
• Final velocity (\(v_f = 17.0 \text{ m/s}\))
• Time (\(t = 8.00 \text{ s}\))

From the formula \(a = \frac{v_f - v_i}{t}\), we find the car is decelerating at \(-1.25 \text{ m/s}^2\), indicating it is slowing down.
This deceleration value will be crucial for calculating the net force.

The net force is the total force acting on an object after all individual forces are combined. Newton's Second Law of Motion tells us that an object's force is the product of its mass and acceleration, given by \(F = m \cdot a\). In our exercise, once we know the mass of the car and its deceleration, we can calculate the force causing this change in velocity. Here, the car's mass is \(1380 \text{ kg}\) and the deceleration we already calculated is \(-1.25 \text{ m/s}^2\).
Using these values, the net force is:

• Mass (\(m = 1380 \text{ kg}\))
• Acceleration (\(a = -1.25 \text{ m/s}^2\))

The net force is calculated by multiplying the mass by the acceleration producing \(-1725 \text{ N}\). The negative sign indicates the force direction will be further explained.

Velocity change is a crucial factor in understanding motion dynamics. It tells us how quickly and in what direction an object changes its speed over time. Velocity has both magnitude and direction, making it a vector quantity. In the problem, the car's velocity changes from \(27.0 \text{ m/s}\) to \(17.0 \text{ m/s}\).
This transition over \(8.00 \text{ s}\) highlights a decrease in speed, implying the vehicle is slowing down. The change in velocity is essential for calculating acceleration, as it reflects how fast the car has slowed over that period. By determining this change, we can further understand the forces involved. Specifically, in this context, the initial velocity is greater than the final, signifying deceleration.

The direction of force is vital for understanding how an object interacts with its environment. Force has both magnitude and direction. In this exercise, since the calculated net force (\(-1725 \text{ N}\)) is negative, it shows the force acts in the opposite direction of the car's initial movement. Initially, the car moves east, and a negative force suggests it's acting west, causing the car to decelerate.
When examining the direction:

• Positive force direction: Same as initial movement (here, east).
• Negative force direction: Opposite to initial movement (here, west).

Thus, the force responsible for slowing the car acts to the west.